{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0001","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-12, -11, -10}，f:D→R，f(x)=(-2)x+(-1)。點 (-9, 17) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=17。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036001,"parameters":{"A":[-12,-11,-10],"m":-2,"b":-1,"domain":"reals","operation":"graph_membership","x":-9,"y":17,"semantic_template":"qf-function-graph-membership/{\"A\":[-12,-11,-10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-9,\"y\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0002","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-11, -10, -9}，f:D→R，f(x)=(-1)x+(0)。點 (-10, 11) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=10。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036002,"parameters":{"A":[-11,-10,-9],"m":-1,"b":0,"domain":"reals","operation":"graph_membership","x":-10,"y":11,"semantic_template":"qf-function-graph-membership/{\"A\":[-11,-10,-9],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":-10,\"y\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0003","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-10, -9, -8}，f:D→R，f(x)=(0)x+(1)。點 (-8, 1) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=1。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036003,"parameters":{"A":[-10,-9,-8],"m":0,"b":1,"domain":"reals","operation":"graph_membership","x":-8,"y":1,"semantic_template":"qf-function-graph-membership/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":-8,\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0004","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-9, -8, -7}，f:D→R，f(x)=(1)x+(2)。點 (-6, -4) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=-4。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036004,"parameters":{"A":[-9,-8,-7],"m":1,"b":2,"domain":"reals","operation":"graph_membership","x":-6,"y":-4,"semantic_template":"qf-function-graph-membership/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":-6,\"y\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0005","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-8, -7, -6}，f:D→R，f(x)=(2)x+(-1)。點 (-7, -14) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=-15。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036005,"parameters":{"A":[-8,-7,-6],"m":2,"b":-1,"domain":"reals","operation":"graph_membership","x":-7,"y":-14,"semantic_template":"qf-function-graph-membership/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":-7,\"y\":-14}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0006","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-7, -6, -5}，f:D→R，f(x)=(-2)x+(0)。點 (-5, 10) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=10。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036006,"parameters":{"A":[-7,-6,-5],"m":-2,"b":0,"domain":"reals","operation":"graph_membership","x":-5,"y":10,"semantic_template":"qf-function-graph-membership/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-5,\"y\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0007","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-6, -5, -4}，f:D→R，f(x)=(-1)x+(1)。點 (-3, 4) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=4。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036007,"parameters":{"A":[-6,-5,-4],"m":-1,"b":1,"domain":"reals","operation":"graph_membership","x":-3,"y":4,"semantic_template":"qf-function-graph-membership/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":-3,\"y\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0008","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-5, -4, -3}，f:D→R，f(x)=(0)x+(2)。點 (-4, 3) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=2。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036008,"parameters":{"A":[-5,-4,-3],"m":0,"b":2,"domain":"reals","operation":"graph_membership","x":-4,"y":3,"semantic_template":"qf-function-graph-membership/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":-4,\"y\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0009","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-4, -3, -2}，f:D→R，f(x)=(1)x+(-1)。點 (-2, -3) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=-3。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036009,"parameters":{"A":[-4,-3,-2],"m":1,"b":-1,"domain":"reals","operation":"graph_membership","x":-2,"y":-3,"semantic_template":"qf-function-graph-membership/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":-2,\"y\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0010","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-3, -2, -1}，f:D→R，f(x)=(2)x+(0)。點 (0, 0) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=0。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036010,"parameters":{"A":[-3,-2,-1],"m":2,"b":0,"domain":"reals","operation":"graph_membership","x":0,"y":0,"semantic_template":"qf-function-graph-membership/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":0,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0011","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-2, -1, 0}，f:D→R，f(x)=(-2)x+(1)。點 (-1, 4) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=3。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036011,"parameters":{"A":[-2,-1,0],"m":-2,"b":1,"domain":"reals","operation":"graph_membership","x":-1,"y":4,"semantic_template":"qf-function-graph-membership/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-1,\"y\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0012","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={-1, 0, 1}，f:D→R，f(x)=(-1)x+(2)。點 (1, 1) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=1。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036012,"parameters":{"A":[-1,0,1],"m":-1,"b":2,"domain":"reals","operation":"graph_membership","x":1,"y":1,"semantic_template":"qf-function-graph-membership/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":1,\"y\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0013","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={0, 1, 2}，f:D→R，f(x)=(0)x+(-1)。點 (3, -1) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=-1。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036013,"parameters":{"A":[0,1,2],"m":0,"b":-1,"domain":"reals","operation":"graph_membership","x":3,"y":-1,"semantic_template":"qf-function-graph-membership/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":3,\"y\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0014","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={1, 2, 3}，f:D→R，f(x)=(1)x+(0)。點 (2, 3) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=2。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036014,"parameters":{"A":[1,2,3],"m":1,"b":0,"domain":"reals","operation":"graph_membership","x":2,"y":3,"semantic_template":"qf-function-graph-membership/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":2,\"y\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0015","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={2, 3, 4}，f:D→R，f(x)=(2)x+(1)。點 (4, 9) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=9。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036015,"parameters":{"A":[2,3,4],"m":2,"b":1,"domain":"reals","operation":"graph_membership","x":4,"y":9,"semantic_template":"qf-function-graph-membership/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":4,\"y\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0016","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={3, 4, 5}，f:D→R，f(x)=(-2)x+(2)。點 (6, -10) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=-10。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036016,"parameters":{"A":[3,4,5],"m":-2,"b":2,"domain":"reals","operation":"graph_membership","x":6,"y":-10,"semantic_template":"qf-function-graph-membership/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":6,\"y\":-10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0017","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={4, 5, 6}，f:D→R，f(x)=(-1)x+(-1)。點 (5, -5) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=-6。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036017,"parameters":{"A":[4,5,6],"m":-1,"b":-1,"domain":"reals","operation":"graph_membership","x":5,"y":-5,"semantic_template":"qf-function-graph-membership/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":5,\"y\":-5}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0018","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={5, 6, 7}，f:D→R，f(x)=(0)x+(0)。點 (7, 0) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=0。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036018,"parameters":{"A":[5,6,7],"m":0,"b":0,"domain":"reals","operation":"graph_membership","x":7,"y":0,"semantic_template":"qf-function-graph-membership/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":7,\"y\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0019","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={6, 7, 8}，f:D→R，f(x)=(1)x+(1)。點 (9, 10) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=10。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036019,"parameters":{"A":[6,7,8],"m":1,"b":1,"domain":"reals","operation":"graph_membership","x":9,"y":10,"semantic_template":"qf-function-graph-membership/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":9,\"y\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0020","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={7, 8, 9}，f:D→R，f(x)=(2)x+(2)。點 (8, 19) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=18。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036020,"parameters":{"A":[7,8,9],"m":2,"b":2,"domain":"reals","operation":"graph_membership","x":8,"y":19,"semantic_template":"qf-function-graph-membership/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":8,\"y\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0021","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={8, 9, 10}，f:D→R，f(x)=(-2)x+(-1)。點 (10, -21) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=-21。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036021,"parameters":{"A":[8,9,10],"m":-2,"b":-1,"domain":"reals","operation":"graph_membership","x":10,"y":-21,"semantic_template":"qf-function-graph-membership/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":10,\"y\":-21}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0022","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={9, 10, 11}，f:D→R，f(x)=(-1)x+(0)。點 (12, -12) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=-12。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036022,"parameters":{"A":[9,10,11],"m":-1,"b":0,"domain":"reals","operation":"graph_membership","x":12,"y":-12,"semantic_template":"qf-function-graph-membership/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":12,\"y\":-12}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0023","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={10, 11, 12}，f:D→R，f(x)=(0)x+(1)。點 (11, 2) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=是；mx+b=1。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036023,"parameters":{"A":[10,11,12],"m":0,"b":1,"domain":"reals","operation":"graph_membership","x":11,"y":2,"semantic_template":"qf-function-graph-membership/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":11,\"y\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0024","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={11, 12, 13}，f:D→R，f(x)=(1)x+(2)。點 (13, 15) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"x∈D=是；mx+b=15。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036024,"parameters":{"A":[11,12,13],"m":1,"b":2,"domain":"reals","operation":"graph_membership","x":13,"y":15,"semantic_template":"qf-function-graph-membership/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":13,\"y\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0025","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"含定義域限制的圖形成員","stem_zh":"固定直角座標系，定義域 D={12, 13, 14}，f:D→R，f(x)=(2)x+(-1)。點 (15, 29) 是否屬於宣告圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"x∈D=否；mx+b=29。需同時通過定義域與輸出等式。域外代數式值不是宣告函數在域外的值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["含定義域限制的圖形成員"]},"variant":{"family_id":"qf-function-graph-membership","seed":202610036025,"parameters":{"A":[12,13,14],"m":2,"b":-1,"domain":"reals","operation":"graph_membership","x":15,"y":29,"semantic_template":"qf-function-graph-membership/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":15,\"y\":29}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0026","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-12, -11, -10}，f:D→R，f(x)=(-2)x+(-1)。合法輸入 -12 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-12, 23)","explanation_zh":"對應點為 (-12, 23)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036026,"parameters":{"A":[-12,-11,-10],"m":-2,"b":-1,"domain":"reals","operation":"graph_point","x":-12,"semantic_template":"qf-function-graph-point/{\"A\":[-12,-11,-10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0027","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-11, -10, -9}，f:D→R，f(x)=(-1)x+(0)。合法輸入 -10 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-10, 10)","explanation_zh":"對應點為 (-10, 10)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036027,"parameters":{"A":[-11,-10,-9],"m":-1,"b":0,"domain":"reals","operation":"graph_point","x":-10,"semantic_template":"qf-function-graph-point/{\"A\":[-11,-10,-9],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0028","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-10, -9, -8}，f:D→R，f(x)=(0)x+(1)。合法輸入 -8 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-8, 1)","explanation_zh":"對應點為 (-8, 1)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036028,"parameters":{"A":[-10,-9,-8],"m":0,"b":1,"domain":"reals","operation":"graph_point","x":-8,"semantic_template":"qf-function-graph-point/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0029","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-9, -8, -7}，f:D→R，f(x)=(1)x+(2)。合法輸入 -9 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-9, -7)","explanation_zh":"對應點為 (-9, -7)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036029,"parameters":{"A":[-9,-8,-7],"m":1,"b":2,"domain":"reals","operation":"graph_point","x":-9,"semantic_template":"qf-function-graph-point/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0030","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-8, -7, -6}，f:D→R，f(x)=(2)x+(-1)。合法輸入 -7 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-7, -15)","explanation_zh":"對應點為 (-7, -15)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036030,"parameters":{"A":[-8,-7,-6],"m":2,"b":-1,"domain":"reals","operation":"graph_point","x":-7,"semantic_template":"qf-function-graph-point/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0031","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-7, -6, -5}，f:D→R，f(x)=(-2)x+(0)。合法輸入 -5 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-5, 10)","explanation_zh":"對應點為 (-5, 10)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036031,"parameters":{"A":[-7,-6,-5],"m":-2,"b":0,"domain":"reals","operation":"graph_point","x":-5,"semantic_template":"qf-function-graph-point/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0032","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-6, -5, -4}，f:D→R，f(x)=(-1)x+(1)。合法輸入 -6 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-6, 7)","explanation_zh":"對應點為 (-6, 7)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036032,"parameters":{"A":[-6,-5,-4],"m":-1,"b":1,"domain":"reals","operation":"graph_point","x":-6,"semantic_template":"qf-function-graph-point/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0033","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-5, -4, -3}，f:D→R，f(x)=(0)x+(2)。合法輸入 -4 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-4, 2)","explanation_zh":"對應點為 (-4, 2)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036033,"parameters":{"A":[-5,-4,-3],"m":0,"b":2,"domain":"reals","operation":"graph_point","x":-4,"semantic_template":"qf-function-graph-point/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0034","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-4, -3, -2}，f:D→R，f(x)=(1)x+(-1)。合法輸入 -2 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-2, -3)","explanation_zh":"對應點為 (-2, -3)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036034,"parameters":{"A":[-4,-3,-2],"m":1,"b":-1,"domain":"reals","operation":"graph_point","x":-2,"semantic_template":"qf-function-graph-point/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0035","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-3, -2, -1}，f:D→R，f(x)=(2)x+(0)。合法輸入 -3 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-3, -6)","explanation_zh":"對應點為 (-3, -6)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036035,"parameters":{"A":[-3,-2,-1],"m":2,"b":0,"domain":"reals","operation":"graph_point","x":-3,"semantic_template":"qf-function-graph-point/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0036","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-2, -1, 0}，f:D→R，f(x)=(-2)x+(1)。合法輸入 -1 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(-1, 3)","explanation_zh":"對應點為 (-1, 3)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036036,"parameters":{"A":[-2,-1,0],"m":-2,"b":1,"domain":"reals","operation":"graph_point","x":-1,"semantic_template":"qf-function-graph-point/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0037","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={-1, 0, 1}，f:D→R，f(x)=(-1)x+(2)。合法輸入 1 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(1, 1)","explanation_zh":"對應點為 (1, 1)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036037,"parameters":{"A":[-1,0,1],"m":-1,"b":2,"domain":"reals","operation":"graph_point","x":1,"semantic_template":"qf-function-graph-point/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0038","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={0, 1, 2}，f:D→R，f(x)=(0)x+(-1)。合法輸入 0 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(0, -1)","explanation_zh":"對應點為 (0, -1)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036038,"parameters":{"A":[0,1,2],"m":0,"b":-1,"domain":"reals","operation":"graph_point","x":0,"semantic_template":"qf-function-graph-point/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0039","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={1, 2, 3}，f:D→R，f(x)=(1)x+(0)。合法輸入 2 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(2, 2)","explanation_zh":"對應點為 (2, 2)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036039,"parameters":{"A":[1,2,3],"m":1,"b":0,"domain":"reals","operation":"graph_point","x":2,"semantic_template":"qf-function-graph-point/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0040","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={2, 3, 4}，f:D→R，f(x)=(2)x+(1)。合法輸入 4 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(4, 9)","explanation_zh":"對應點為 (4, 9)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036040,"parameters":{"A":[2,3,4],"m":2,"b":1,"domain":"reals","operation":"graph_point","x":4,"semantic_template":"qf-function-graph-point/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0041","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={3, 4, 5}，f:D→R，f(x)=(-2)x+(2)。合法輸入 3 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(3, -4)","explanation_zh":"對應點為 (3, -4)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036041,"parameters":{"A":[3,4,5],"m":-2,"b":2,"domain":"reals","operation":"graph_point","x":3,"semantic_template":"qf-function-graph-point/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0042","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={4, 5, 6}，f:D→R，f(x)=(-1)x+(-1)。合法輸入 5 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(5, -6)","explanation_zh":"對應點為 (5, -6)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036042,"parameters":{"A":[4,5,6],"m":-1,"b":-1,"domain":"reals","operation":"graph_point","x":5,"semantic_template":"qf-function-graph-point/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0043","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={5, 6, 7}，f:D→R，f(x)=(0)x+(0)。合法輸入 7 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(7, 0)","explanation_zh":"對應點為 (7, 0)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036043,"parameters":{"A":[5,6,7],"m":0,"b":0,"domain":"reals","operation":"graph_point","x":7,"semantic_template":"qf-function-graph-point/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0044","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={6, 7, 8}，f:D→R，f(x)=(1)x+(1)。合法輸入 6 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(6, 7)","explanation_zh":"對應點為 (6, 7)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036044,"parameters":{"A":[6,7,8],"m":1,"b":1,"domain":"reals","operation":"graph_point","x":6,"semantic_template":"qf-function-graph-point/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0045","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={7, 8, 9}，f:D→R，f(x)=(2)x+(2)。合法輸入 8 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(8, 18)","explanation_zh":"對應點為 (8, 18)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036045,"parameters":{"A":[7,8,9],"m":2,"b":2,"domain":"reals","operation":"graph_point","x":8,"semantic_template":"qf-function-graph-point/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0046","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={8, 9, 10}，f:D→R，f(x)=(-2)x+(-1)。合法輸入 10 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(10, -21)","explanation_zh":"對應點為 (10, -21)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036046,"parameters":{"A":[8,9,10],"m":-2,"b":-1,"domain":"reals","operation":"graph_point","x":10,"semantic_template":"qf-function-graph-point/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0047","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={9, 10, 11}，f:D→R，f(x)=(-1)x+(0)。合法輸入 9 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(9, -9)","explanation_zh":"對應點為 (9, -9)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036047,"parameters":{"A":[9,10,11],"m":-1,"b":0,"domain":"reals","operation":"graph_point","x":9,"semantic_template":"qf-function-graph-point/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0048","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={10, 11, 12}，f:D→R，f(x)=(0)x+(1)。合法輸入 11 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(11, 1)","explanation_zh":"對應點為 (11, 1)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036048,"parameters":{"A":[10,11,12],"m":0,"b":1,"domain":"reals","operation":"graph_point","x":11,"semantic_template":"qf-function-graph-point/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0049","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={11, 12, 13}，f:D→R，f(x)=(1)x+(2)。合法輸入 13 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(13, 15)","explanation_zh":"對應點為 (13, 15)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036049,"parameters":{"A":[11,12,13],"m":1,"b":2,"domain":"reals","operation":"graph_point","x":13,"semantic_template":"qf-function-graph-point/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0050","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"輸入對應的函數圖形點","stem_zh":"固定直角座標系，定義域 D={12, 13, 14}，f:D→R，f(x)=(2)x+(-1)。合法輸入 12 對應圖形上的哪個有序對？","answer":{"kind":"expression","value":"(12, 23)","explanation_zh":"對應點為 (12, 23)。輸入屬於定義域，第一座標放輸入、第二座標放唯一輸出。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["輸入對應的函數圖形點"]},"variant":{"family_id":"qf-function-graph-point","seed":202610036050,"parameters":{"A":[12,13,14],"m":2,"b":-1,"domain":"reals","operation":"graph_point","x":12,"semantic_template":"qf-function-graph-point/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0051","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D=∅，f:D→R，f(x)=(-2)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"∅","explanation_zh":"圖形是 ∅。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036051,"parameters":{"A":[],"m":-2,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0052","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={0}，f:D→R，f(x)=(-1)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(0, 0)}","explanation_zh":"圖形是 {(0, 0)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036052,"parameters":{"A":[0],"m":-1,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[0],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0053","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-10, -9, -8}，f:D→R，f(x)=(0)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-10, 1), (-9, 1), (-8, 1)}","explanation_zh":"圖形是 {(-10, 1), (-9, 1), (-8, 1)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036053,"parameters":{"A":[-10,-9,-8],"m":0,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0054","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-9, -8, -7}，f:D→R，f(x)=(1)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-9, -7), (-8, -6), (-7, -5)}","explanation_zh":"圖形是 {(-9, -7), (-8, -6), (-7, -5)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036054,"parameters":{"A":[-9,-8,-7],"m":1,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0055","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-8, -7, -6}，f:D→R，f(x)=(2)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-8, -17), (-7, -15), (-6, -13)}","explanation_zh":"圖形是 {(-8, -17), (-7, -15), (-6, -13)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036055,"parameters":{"A":[-8,-7,-6],"m":2,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0056","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-7, -6, -5}，f:D→R，f(x)=(-2)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-7, 14), (-6, 12), (-5, 10)}","explanation_zh":"圖形是 {(-7, 14), (-6, 12), (-5, 10)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036056,"parameters":{"A":[-7,-6,-5],"m":-2,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0057","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-6, -5, -4}，f:D→R，f(x)=(-1)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-6, 7), (-5, 6), (-4, 5)}","explanation_zh":"圖形是 {(-6, 7), (-5, 6), (-4, 5)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036057,"parameters":{"A":[-6,-5,-4],"m":-1,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0058","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-5, -4, -3}，f:D→R，f(x)=(0)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-5, 2), (-4, 2), (-3, 2)}","explanation_zh":"圖形是 {(-5, 2), (-4, 2), (-3, 2)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036058,"parameters":{"A":[-5,-4,-3],"m":0,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0059","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-4, -3, -2}，f:D→R，f(x)=(1)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-4, -5), (-3, -4), (-2, -3)}","explanation_zh":"圖形是 {(-4, -5), (-3, -4), (-2, -3)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036059,"parameters":{"A":[-4,-3,-2],"m":1,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0060","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-3, -2, -1}，f:D→R，f(x)=(2)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-3, -6), (-2, -4), (-1, -2)}","explanation_zh":"圖形是 {(-3, -6), (-2, -4), (-1, -2)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036060,"parameters":{"A":[-3,-2,-1],"m":2,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0061","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-2, -1, 0}，f:D→R，f(x)=(-2)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-2, 5), (-1, 3), (0, 1)}","explanation_zh":"圖形是 {(-2, 5), (-1, 3), (0, 1)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036061,"parameters":{"A":[-2,-1,0],"m":-2,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0062","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={-1, 0, 1}，f:D→R，f(x)=(-1)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(-1, 3), (0, 2), (1, 1)}","explanation_zh":"圖形是 {(-1, 3), (0, 2), (1, 1)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036062,"parameters":{"A":[-1,0,1],"m":-1,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0063","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={0, 1, 2}，f:D→R，f(x)=(0)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(0, -1), (1, -1), (2, -1)}","explanation_zh":"圖形是 {(0, -1), (1, -1), (2, -1)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036063,"parameters":{"A":[0,1,2],"m":0,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0064","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={1, 2, 3}，f:D→R，f(x)=(1)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(1, 1), (2, 2), (3, 3)}","explanation_zh":"圖形是 {(1, 1), (2, 2), (3, 3)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036064,"parameters":{"A":[1,2,3],"m":1,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0065","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={2, 3, 4}，f:D→R，f(x)=(2)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(2, 5), (3, 7), (4, 9)}","explanation_zh":"圖形是 {(2, 5), (3, 7), (4, 9)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036065,"parameters":{"A":[2,3,4],"m":2,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0066","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={3, 4, 5}，f:D→R，f(x)=(-2)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(3, -4), (4, -6), (5, -8)}","explanation_zh":"圖形是 {(3, -4), (4, -6), (5, -8)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036066,"parameters":{"A":[3,4,5],"m":-2,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0067","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={4, 5, 6}，f:D→R，f(x)=(-1)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(4, -5), (5, -6), (6, -7)}","explanation_zh":"圖形是 {(4, -5), (5, -6), (6, -7)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036067,"parameters":{"A":[4,5,6],"m":-1,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0068","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={5, 6, 7}，f:D→R，f(x)=(0)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(5, 0), (6, 0), (7, 0)}","explanation_zh":"圖形是 {(5, 0), (6, 0), (7, 0)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036068,"parameters":{"A":[5,6,7],"m":0,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0069","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={6, 7, 8}，f:D→R，f(x)=(1)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(6, 7), (7, 8), (8, 9)}","explanation_zh":"圖形是 {(6, 7), (7, 8), (8, 9)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036069,"parameters":{"A":[6,7,8],"m":1,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0070","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={7, 8, 9}，f:D→R，f(x)=(2)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(7, 16), (8, 18), (9, 20)}","explanation_zh":"圖形是 {(7, 16), (8, 18), (9, 20)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036070,"parameters":{"A":[7,8,9],"m":2,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0071","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={8, 9, 10}，f:D→R，f(x)=(-2)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(8, -17), (9, -19), (10, -21)}","explanation_zh":"圖形是 {(8, -17), (9, -19), (10, -21)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036071,"parameters":{"A":[8,9,10],"m":-2,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0072","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={9, 10, 11}，f:D→R，f(x)=(-1)x+(0)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(9, -9), (10, -10), (11, -11)}","explanation_zh":"圖形是 {(9, -9), (10, -10), (11, -11)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036072,"parameters":{"A":[9,10,11],"m":-1,"b":0,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0073","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={10, 11, 12}，f:D→R，f(x)=(0)x+(1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(10, 1), (11, 1), (12, 1)}","explanation_zh":"圖形是 {(10, 1), (11, 1), (12, 1)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036073,"parameters":{"A":[10,11,12],"m":0,"b":1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0074","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={11, 12, 13}，f:D→R，f(x)=(1)x+(2)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(11, 13), (12, 14), (13, 15)}","explanation_zh":"圖形是 {(11, 13), (12, 14), (13, 15)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036074,"parameters":{"A":[11,12,13],"m":1,"b":2,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0075","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"列出有限函數圖形","stem_zh":"固定直角座標系，定義域 D={12, 13, 14}，f:D→R，f(x)=(2)x+(-1)。按第一座標遞增列出完整函數圖形，重複點只列一次。","answer":{"kind":"expression","value":"{(12, 23), (13, 25), (14, 27)}","explanation_zh":"圖形是 {(12, 23), (13, 25), (14, 27)}。對定義域的每個輸入各列 (x,f(x))；空定義域的圖形為 ∅。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["列出有限函數圖形"]},"variant":{"family_id":"qf-function-graph-finite-set","seed":202610036075,"parameters":{"A":[12,13,14],"m":2,"b":-1,"domain":"reals","operation":"graph_set","semantic_template":"qf-function-graph-finite-set/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0076","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D=∅、陪域 B=∅。有序對集合 ∅ 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"總函數=是。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036076,"parameters":{"A":[],"B":[],"pairs":[],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[],\"B\":[],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0077","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-27, -26}、陪域 B={-9, -8, -7}。有序對集合 {(-27, -9)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036077,"parameters":{"A":[-27,-26],"B":[-9,-8,-7],"pairs":[[-27,-9]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-27,-26],\"B\":[-9,-8,-7],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-27,-9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0078","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-24, -23}、陪域 B={-8, -7, -6}。有序對集合 {(-24, -8), (-24, -6), (-23, -7)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036078,"parameters":{"A":[-24,-23],"B":[-8,-7,-6],"pairs":[[-24,-8],[-23,-7],[-24,-6]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-24,-23],\"B\":[-8,-7,-6],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-24,-8],[-24,-6],[-23,-7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0079","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-21, -20}、陪域 B={-7, -6, -5}。有序對集合 {(-21, -7), (-20, 33)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036079,"parameters":{"A":[-21,-20],"B":[-7,-6,-5],"pairs":[[-21,-7],[-20,33]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-21,-20],\"B\":[-7,-6,-5],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-21,-7],[-20,33]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0080","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-18, -17}、陪域 B={-6, -5, -4}。有序對集合 {(-18, -6), (-17, -5), (-16, -6)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036080,"parameters":{"A":[-18,-17],"B":[-6,-5,-4],"pairs":[[-18,-6],[-17,-5],[-16,-6]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-18,-17],\"B\":[-6,-5,-4],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-18,-6],[-17,-5],[-16,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0081","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-15, -14}、陪域 B={-5, -4, -3}。有序對集合 {(-15, -5), (-14, -4)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"總函數=是。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036081,"parameters":{"A":[-15,-14],"B":[-5,-4,-3],"pairs":[[-15,-5],[-14,-4]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-15,-14],\"B\":[-5,-4,-3],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-15,-5],[-14,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0082","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-12, -11}、陪域 B={-4, -3, -2}。有序對集合 {(-12, -4)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036082,"parameters":{"A":[-12,-11],"B":[-4,-3,-2],"pairs":[[-12,-4]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-12,-11],\"B\":[-4,-3,-2],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-12,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0083","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-9, -8}、陪域 B={-3, -2, -1}。有序對集合 {(-9, -3), (-9, -1), (-8, -2)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036083,"parameters":{"A":[-9,-8],"B":[-3,-2,-1],"pairs":[[-9,-3],[-8,-2],[-9,-1]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-9,-8],\"B\":[-3,-2,-1],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-9,-3],[-9,-1],[-8,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0084","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-6, -5}、陪域 B={-2, -1, 0}。有序對集合 {(-6, -2), (-5, 38)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036084,"parameters":{"A":[-6,-5],"B":[-2,-1,0],"pairs":[[-6,-2],[-5,38]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-6,-5],\"B\":[-2,-1,0],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-6,-2],[-5,38]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0085","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={-3, -2}、陪域 B={-1, 0, 1}。有序對集合 {(-3, -1), (-2, 0), (-1, -1)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036085,"parameters":{"A":[-3,-2],"B":[-1,0,1],"pairs":[[-3,-1],[-2,0],[-1,-1]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[-3,-2],\"B\":[-1,0,1],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-3,-1],[-2,0],[-1,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0086","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={0, 1}、陪域 B={0, 1, 2}。有序對集合 {(0, 0), (1, 1)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"總函數=是。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036086,"parameters":{"A":[0,1],"B":[0,1,2],"pairs":[[0,0],[1,1]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[0,1],\"B\":[0,1,2],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0087","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={3, 4}、陪域 B={1, 2, 3}。有序對集合 {(3, 1)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036087,"parameters":{"A":[3,4],"B":[1,2,3],"pairs":[[3,1]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[3,4],\"B\":[1,2,3],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0088","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={6, 7}、陪域 B={2, 3, 4}。有序對集合 {(6, 2), (6, 4), (7, 3)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036088,"parameters":{"A":[6,7],"B":[2,3,4],"pairs":[[6,2],[7,3],[6,4]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[6,7],\"B\":[2,3,4],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[6,2],[6,4],[7,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0089","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={9, 10}、陪域 B={3, 4, 5}。有序對集合 {(9, 3), (10, 43)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036089,"parameters":{"A":[9,10],"B":[3,4,5],"pairs":[[9,3],[10,43]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[9,10],\"B\":[3,4,5],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[9,3],[10,43]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0090","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={12, 13}、陪域 B={4, 5, 6}。有序對集合 {(12, 4), (13, 5), (14, 4)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036090,"parameters":{"A":[12,13],"B":[4,5,6],"pairs":[[12,4],[13,5],[14,4]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[12,13],\"B\":[4,5,6],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[12,4],[13,5],[14,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0091","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={15, 16}、陪域 B={5, 6, 7}。有序對集合 {(15, 5), (16, 6)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"總函數=是。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036091,"parameters":{"A":[15,16],"B":[5,6,7],"pairs":[[15,5],[16,6]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[15,16],\"B\":[5,6,7],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[15,5],[16,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0092","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={18, 19}、陪域 B={6, 7, 8}。有序對集合 {(18, 6)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036092,"parameters":{"A":[18,19],"B":[6,7,8],"pairs":[[18,6]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[18,19],\"B\":[6,7,8],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[18,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0093","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={21, 22}、陪域 B={7, 8, 9}。有序對集合 {(21, 7), (21, 9), (22, 8)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036093,"parameters":{"A":[21,22],"B":[7,8,9],"pairs":[[21,7],[22,8],[21,9]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[21,22],\"B\":[7,8,9],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[21,7],[21,9],[22,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0094","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={24, 25}、陪域 B={8, 9, 10}。有序對集合 {(24, 8), (25, 48)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036094,"parameters":{"A":[24,25],"B":[8,9,10],"pairs":[[24,8],[25,48]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[24,25],\"B\":[8,9,10],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[24,8],[25,48]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0095","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={27, 28}、陪域 B={9, 10, 11}。有序對集合 {(27, 9), (28, 10), (29, 9)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036095,"parameters":{"A":[27,28],"B":[9,10,11],"pairs":[[27,9],[28,10],[29,9]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[27,28],\"B\":[9,10,11],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[27,9],[28,10],[29,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0096","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={30, 31}、陪域 B={10, 11, 12}。有序對集合 {(30, 10), (31, 11)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"是","explanation_zh":"總函數=是。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036096,"parameters":{"A":[30,31],"B":[10,11,12],"pairs":[[30,10],[31,11]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[30,31],\"B\":[10,11,12],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[30,10],[31,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0097","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={33, 34}、陪域 B={11, 12, 13}。有序對集合 {(33, 11)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036097,"parameters":{"A":[33,34],"B":[11,12,13],"pairs":[[33,11]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[33,34],\"B\":[11,12,13],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[33,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0098","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={36, 37}、陪域 B={12, 13, 14}。有序對集合 {(36, 12), (36, 14), (37, 13)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036098,"parameters":{"A":[36,37],"B":[12,13,14],"pairs":[[36,12],[37,13],[36,14]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[36,37],\"B\":[12,13,14],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[36,12],[36,14],[37,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0099","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={39, 40}、陪域 B={13, 14, 15}。有序對集合 {(39, 13), (40, 53)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036099,"parameters":{"A":[39,40],"B":[13,14,15],"pairs":[[39,13],[40,53]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[39,40],\"B\":[13,14,15],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[39,13],[40,53]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r06-function-graph-0100","batch_id":"batch-20261003-r06-function-graph-foundations","language":"zh-Hant","source_mko_ids":["mko-function-graph"],"title_zh":"有限總函數圖形合法性","stem_zh":"明示定義域 D={42, 43}、陪域 B={14, 15, 16}。有序對集合 {(42, 14), (43, 15), (44, 14)} 是否正好是某個總函數 D→B 的圖形？","answer":{"kind":"short_text","value":"否","explanation_zh":"總函數=否。須讓定義域每個輸入恰有一個陪域內輸出，且不得多出域外點；垂直線至多一點不保證總定義性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限總函數圖形合法性"]},"variant":{"family_id":"qf-function-graph-table-validity","seed":202610036100,"parameters":{"A":[42,43],"B":[14,15,16],"pairs":[[42,14],[43,15],[44,14]],"domain":"reals","operation":"graph_validity","semantic_template":"qf-function-graph-table-validity/{\"A\":[42,43],\"B\":[14,15,16],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[42,14],[43,15],[44,14]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}