{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0001","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a13fb5ebacf597cdc4a66446cab8c867f571986eaa1c46eec51c5fe8d6a5af45","family_id":"qf-function-graph-membership","seed":202610036001,"semantic_template":"qf-function-graph-membership/{\"A\":[-12,-11,-10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-9,\"y\":17}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-12, -11, -10} and f:D→R is given by f(x)=(-2)x+(-1). Does (-9, 17) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -9 does not belong to D, and the formula value is 17. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0002","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b0263a0e9b903c22287eada7def72db184f3960f0abfbfff021e72d2b72587f","family_id":"qf-function-graph-membership","seed":202610036002,"semantic_template":"qf-function-graph-membership/{\"A\":[-11,-10,-9],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":-10,\"y\":11}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Does (-10, 11) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -10 belongs to D, and the formula value is 10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0003","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc6712ac23b50e9091c767f040cd5fbb3cd2b85b469de38ef3506f2101040130","family_id":"qf-function-graph-membership","seed":202610036003,"semantic_template":"qf-function-graph-membership/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":-8,\"y\":1}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). Does (-8, 1) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input -8 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0004","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3f0459e37d8c41cffcded09e752a9058f51e4837d627a68e4099fbf8825066e","family_id":"qf-function-graph-membership","seed":202610036004,"semantic_template":"qf-function-graph-membership/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":-6,\"y\":-4}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). Does (-6, -4) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -6 does not belong to D, and the formula value is -4. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0005","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bdb72935df92b2ea1e1ec8a209207a557ec796112de158bb2dd5e1636bad5a3","family_id":"qf-function-graph-membership","seed":202610036005,"semantic_template":"qf-function-graph-membership/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":-7,\"y\":-14}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). Does (-7, -14) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -7 belongs to D, and the formula value is -15. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0006","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c4ab3126337e706c7f8059f5f4d3fb1459f7ac0555535be6febe75eecbbda8a","family_id":"qf-function-graph-membership","seed":202610036006,"semantic_template":"qf-function-graph-membership/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-5,\"y\":10}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). Does (-5, 10) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input -5 belongs to D, and the formula value is 10. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0007","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eee30602b6151ad9f5545b235e8f5bbf8faed9c5ad70048ff821e00e4c1aab8a","family_id":"qf-function-graph-membership","seed":202610036007,"semantic_template":"qf-function-graph-membership/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":-3,\"y\":4}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). Does (-3, 4) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -3 does not belong to D, and the formula value is 4. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0008","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65c33743cc9fed8a6e585f2b65020ac44e48d421c206582ece97753f3f10295b","family_id":"qf-function-graph-membership","seed":202610036008,"semantic_template":"qf-function-graph-membership/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":-4,\"y\":3}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). Does (-4, 3) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -4 belongs to D, and the formula value is 2. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0009","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe640131d44dc6d10fefdc8332bd026757f7588ecf27b1bc1bcb069b40c0d3dc","family_id":"qf-function-graph-membership","seed":202610036009,"semantic_template":"qf-function-graph-membership/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":-2,\"y\":-3}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). Does (-2, -3) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input -2 belongs to D, and the formula value is -3. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0010","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8d8616b64604867672014eda7b97e7a3592b3def88cc798895d5311e219c564","family_id":"qf-function-graph-membership","seed":202610036010,"semantic_template":"qf-function-graph-membership/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":0,\"y\":0}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). Does (0, 0) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 0 does not belong to D, and the formula value is 0. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0011","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e892186b2185942c9de2ccc7ca5fa3d1464c1c58e7ffe9abeee20673b4ffc10d","family_id":"qf-function-graph-membership","seed":202610036011,"semantic_template":"qf-function-graph-membership/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":-1,\"y\":4}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). Does (-1, 4) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input -1 belongs to D, and the formula value is 3. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0012","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c399bc3507cbba4df120acd490ca97b1abd3c9d01b2fe61b241024dbaabfff8a","family_id":"qf-function-graph-membership","seed":202610036012,"semantic_template":"qf-function-graph-membership/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":1,\"y\":1}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). Does (1, 1) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input 1 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0013","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"761b9b8a702774764d3ebaeb6f4ef19ecff629c931b7235820e4b3a82cf4b42e","family_id":"qf-function-graph-membership","seed":202610036013,"semantic_template":"qf-function-graph-membership/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":3,\"y\":-1}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). Does (3, -1) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 3 does not belong to D, and the formula value is -1. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0014","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d337192399a87a7d61bfbb88767dc0c53a1cf56b91e378fc7927f2f236e9104d","family_id":"qf-function-graph-membership","seed":202610036014,"semantic_template":"qf-function-graph-membership/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":2,\"y\":3}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). Does (2, 3) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 2 belongs to D, and the formula value is 2. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0015","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b2b72e20116a4b17c90cc3d9448d18bda87340a5cef4fe0cf02d5a34e64efd9","family_id":"qf-function-graph-membership","seed":202610036015,"semantic_template":"qf-function-graph-membership/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":4,\"y\":9}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). Does (4, 9) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input 4 belongs to D, and the formula value is 9. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0016","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59784e59711eaec5f1a353322c9f1f397a293597b4d673c87037d01a166ee627","family_id":"qf-function-graph-membership","seed":202610036016,"semantic_template":"qf-function-graph-membership/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":6,\"y\":-10}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). Does (6, -10) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 6 does not belong to D, and the formula value is -10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0017","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f177e3ba7cb4d6affb8d25cf4aa7ff67617a618c0e496fce6c2b5a52a090bff","family_id":"qf-function-graph-membership","seed":202610036017,"semantic_template":"qf-function-graph-membership/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":5,\"y\":-5}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). Does (5, -5) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 5 belongs to D, and the formula value is -6. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0018","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f3c2663194876778578fc2bd93eaf4864a5533b5e03fbf7de56ce9841379030","family_id":"qf-function-graph-membership","seed":202610036018,"semantic_template":"qf-function-graph-membership/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":7,\"y\":0}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). Does (7, 0) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input 7 belongs to D, and the formula value is 0. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0019","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33ed6593f7cb4511cab68377c122373f56b0344bb68a43259e158fce367ec297","family_id":"qf-function-graph-membership","seed":202610036019,"semantic_template":"qf-function-graph-membership/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":9,\"y\":10}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). Does (9, 10) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 9 does not belong to D, and the formula value is 10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0020","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12fd7438b37b01fa08b4ddccbb49a4d86f6bbe0b6bad9a440e24994d83ef9f53","family_id":"qf-function-graph-membership","seed":202610036020,"semantic_template":"qf-function-graph-membership/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":8,\"y\":19}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). Does (8, 19) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 8 belongs to D, and the formula value is 18. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0021","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d2a58c9ca2ecf27959f5bc732d3836a0383ca4f771023dc15c8765ddcd4ad72","family_id":"qf-function-graph-membership","seed":202610036021,"semantic_template":"qf-function-graph-membership/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_membership\",\"x\":10,\"y\":-21}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Does (10, -21) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input 10 belongs to D, and the formula value is -21. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0022","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"190091ddc2a88e3750396fa4bb486155c74afafcaac1c3feb62fb6590ed3191f","family_id":"qf-function-graph-membership","seed":202610036022,"semantic_template":"qf-function-graph-membership/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_membership\",\"x\":12,\"y\":-12}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). Does (12, -12) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 12 does not belong to D, and the formula value is -12. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0023","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e66588076c4775791de96b73ba7122a70f43f5ca28167f5985fed001b064ed9","family_id":"qf-function-graph-membership","seed":202610036023,"semantic_template":"qf-function-graph-membership/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_membership\",\"x\":11,\"y\":2}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). Does (11, 2) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 11 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0024","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb5c8425988914e90b8e6dbe576cb09793466ccfded7e4cd75bd40f9dd54b3d6","family_id":"qf-function-graph-membership","seed":202610036024,"semantic_template":"qf-function-graph-membership/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_membership\",\"x\":13,\"y\":15}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). Does (13, 15) belong to the declared graph?","answer":{"kind":"short_text","value":"Yes","explanation":"The input 13 belongs to D, and the formula value is 15. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0025","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cbab2a9296a0526514d2b52a595cbeec3e169ea17b5afb051351ef2b14cdce5b","family_id":"qf-function-graph-membership","seed":202610036025,"semantic_template":"qf-function-graph-membership/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_membership\",\"x\":15,\"y\":29}"},"fields":{"title":"Graph Membership with a Domain Restriction","stem":"In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). Does (15, 29) belong to the declared graph?","answer":{"kind":"short_text","value":"No","explanation":"The input 15 does not belong to D, and the formula value is 29. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there."},"skills":["Graph Membership with a Domain Restriction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0026","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"093c534f1f00d9094567be4613e24a7ddf31abef452d7b06ebc406f095d9b1d8","family_id":"qf-function-graph-point","seed":202610036026,"semantic_template":"qf-function-graph-point/{\"A\":[-12,-11,-10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-12}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-12, -11, -10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input -12?","answer":{"kind":"expression","value":"(-12, 23)","explanation":"The point is (-12, 23). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0027","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf72dba9b3037beea4f3e248359a395f453f241ad136fe349d60758bf1179b48","family_id":"qf-function-graph-point","seed":202610036027,"semantic_template":"qf-function-graph-point/{\"A\":[-11,-10,-9],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":-10}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Which ordered graph point corresponds to the permitted input -10?","answer":{"kind":"expression","value":"(-10, 10)","explanation":"The point is (-10, 10). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0028","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"240922f683c92f84702a48bfd811b9273010d6e5d79a84acedd79d276b92ef7c","family_id":"qf-function-graph-point","seed":202610036028,"semantic_template":"qf-function-graph-point/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":-8}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). Which ordered graph point corresponds to the permitted input -8?","answer":{"kind":"expression","value":"(-8, 1)","explanation":"The point is (-8, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0029","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c20ce1cb2a1ff186cb35a34699da2e59b782307236d9a27c043ca7e33e89924b","family_id":"qf-function-graph-point","seed":202610036029,"semantic_template":"qf-function-graph-point/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":-9}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). Which ordered graph point corresponds to the permitted input -9?","answer":{"kind":"expression","value":"(-9, -7)","explanation":"The point is (-9, -7). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0030","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5331897916599789d650e4684282721c794aa8251a97a3244ae534174ee5c102","family_id":"qf-function-graph-point","seed":202610036030,"semantic_template":"qf-function-graph-point/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":-7}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). Which ordered graph point corresponds to the permitted input -7?","answer":{"kind":"expression","value":"(-7, -15)","explanation":"The point is (-7, -15). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0031","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52e2bdedf14121c8146e61b70f26f3b3ce618d17edc38242f1bb3ae7583c8fe3","family_id":"qf-function-graph-point","seed":202610036031,"semantic_template":"qf-function-graph-point/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-5}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). Which ordered graph point corresponds to the permitted input -5?","answer":{"kind":"expression","value":"(-5, 10)","explanation":"The point is (-5, 10). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0032","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8f039676e366af7075d2734315502279b0296b8746ea5a742c6e31a872d3b0b","family_id":"qf-function-graph-point","seed":202610036032,"semantic_template":"qf-function-graph-point/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":-6}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). Which ordered graph point corresponds to the permitted input -6?","answer":{"kind":"expression","value":"(-6, 7)","explanation":"The point is (-6, 7). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0033","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6cf9ee2cfaa4cb9e581365b44c9733941e8acf8d26f340cfbef4021925c573b","family_id":"qf-function-graph-point","seed":202610036033,"semantic_template":"qf-function-graph-point/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":-4}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). Which ordered graph point corresponds to the permitted input -4?","answer":{"kind":"expression","value":"(-4, 2)","explanation":"The point is (-4, 2). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0034","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8db6be7042ecefb602f7a5712d16473ff6718fb86e67e157b2c6be52ecf31a9","family_id":"qf-function-graph-point","seed":202610036034,"semantic_template":"qf-function-graph-point/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":-2}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). Which ordered graph point corresponds to the permitted input -2?","answer":{"kind":"expression","value":"(-2, -3)","explanation":"The point is (-2, -3). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0035","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4604a4e5aba0e40c26420360aad50302d87db7e5dcb6cd08699cf6dfcca4f99a","family_id":"qf-function-graph-point","seed":202610036035,"semantic_template":"qf-function-graph-point/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":-3}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). Which ordered graph point corresponds to the permitted input -3?","answer":{"kind":"expression","value":"(-3, -6)","explanation":"The point is (-3, -6). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0036","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"adb542c2e5c829069ec76b350afffff4d84abf761cee9f9297b064a1f861e774","family_id":"qf-function-graph-point","seed":202610036036,"semantic_template":"qf-function-graph-point/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":-1}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). Which ordered graph point corresponds to the permitted input -1?","answer":{"kind":"expression","value":"(-1, 3)","explanation":"The point is (-1, 3). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0037","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d415a45de5af04d4e171d141a1df5b17b64e482ffce755ba3c59b49b202f2389","family_id":"qf-function-graph-point","seed":202610036037,"semantic_template":"qf-function-graph-point/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":1}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). Which ordered graph point corresponds to the permitted input 1?","answer":{"kind":"expression","value":"(1, 1)","explanation":"The point is (1, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0038","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3469246598ceaf393a306e0ef92b281ffc7199509d9d6761c551517a2697e6d4","family_id":"qf-function-graph-point","seed":202610036038,"semantic_template":"qf-function-graph-point/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":0}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). Which ordered graph point corresponds to the permitted input 0?","answer":{"kind":"expression","value":"(0, -1)","explanation":"The point is (0, -1). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0039","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"94e83eba433b8d40b2c6f0f180b184415131b6ac9d99008bfd8dd8e826fcf735","family_id":"qf-function-graph-point","seed":202610036039,"semantic_template":"qf-function-graph-point/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":2}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). Which ordered graph point corresponds to the permitted input 2?","answer":{"kind":"expression","value":"(2, 2)","explanation":"The point is (2, 2). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0040","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1be3a9c947a2d0dcde39764424a3696fe54c9e7a82662cc437b5a7c5a4064d6","family_id":"qf-function-graph-point","seed":202610036040,"semantic_template":"qf-function-graph-point/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":4}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). Which ordered graph point corresponds to the permitted input 4?","answer":{"kind":"expression","value":"(4, 9)","explanation":"The point is (4, 9). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0041","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b1b8f5b54aecdeaa78ce935a2fd8fb82786c85bb7f81befb7cfc387bc2ef172","family_id":"qf-function-graph-point","seed":202610036041,"semantic_template":"qf-function-graph-point/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":3}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). Which ordered graph point corresponds to the permitted input 3?","answer":{"kind":"expression","value":"(3, -4)","explanation":"The point is (3, -4). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0042","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"306eee34d16d524076ddd5bcd72f866b0c4d408fcf2c02f1ae21689168148b2f","family_id":"qf-function-graph-point","seed":202610036042,"semantic_template":"qf-function-graph-point/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":5}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). Which ordered graph point corresponds to the permitted input 5?","answer":{"kind":"expression","value":"(5, -6)","explanation":"The point is (5, -6). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0043","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"323e36c8f9181743508ef660a8ed8c337eb1ab2f612fe603e3cd975bdd870bd9","family_id":"qf-function-graph-point","seed":202610036043,"semantic_template":"qf-function-graph-point/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":7}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). Which ordered graph point corresponds to the permitted input 7?","answer":{"kind":"expression","value":"(7, 0)","explanation":"The point is (7, 0). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0044","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aaa16a97c399ea174261db551976822e387d76d8cbfa755ffe22bb30b60f6650","family_id":"qf-function-graph-point","seed":202610036044,"semantic_template":"qf-function-graph-point/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":6}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). Which ordered graph point corresponds to the permitted input 6?","answer":{"kind":"expression","value":"(6, 7)","explanation":"The point is (6, 7). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0045","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1cb0a5f2a1d5a185571cbf5c93764b0842f8d0e73281a15260abe72272fd7c1e","family_id":"qf-function-graph-point","seed":202610036045,"semantic_template":"qf-function-graph-point/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":8}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). Which ordered graph point corresponds to the permitted input 8?","answer":{"kind":"expression","value":"(8, 18)","explanation":"The point is (8, 18). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0046","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e35cf81784d2f3d63ec53012c406ac40bd6e397976b28d9e13e8a52e5028e6a","family_id":"qf-function-graph-point","seed":202610036046,"semantic_template":"qf-function-graph-point/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_point\",\"x\":10}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input 10?","answer":{"kind":"expression","value":"(10, -21)","explanation":"The point is (10, -21). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0047","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcfc7b2da29c2d8899083531c8d6af7c2be1d64b65d8f44f7a32c7a1716b354b","family_id":"qf-function-graph-point","seed":202610036047,"semantic_template":"qf-function-graph-point/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_point\",\"x\":9}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). Which ordered graph point corresponds to the permitted input 9?","answer":{"kind":"expression","value":"(9, -9)","explanation":"The point is (9, -9). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0048","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1727105f7a5efb7474e4736d8b74fb7b6deeb5bd8091cf0ebab00141a50ec21c","family_id":"qf-function-graph-point","seed":202610036048,"semantic_template":"qf-function-graph-point/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_point\",\"x\":11}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). Which ordered graph point corresponds to the permitted input 11?","answer":{"kind":"expression","value":"(11, 1)","explanation":"The point is (11, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0049","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01af9efeff3c3fc395bd1e06ea981ce67e52ecb0a077c4e1704e1d2d0e514cf7","family_id":"qf-function-graph-point","seed":202610036049,"semantic_template":"qf-function-graph-point/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_point\",\"x\":13}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). Which ordered graph point corresponds to the permitted input 13?","answer":{"kind":"expression","value":"(13, 15)","explanation":"The point is (13, 15). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0050","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1875653f07e9b1f4a50e4315b7a6f6722c2eacdf6a4e8aaa74b6970eb48a3cca","family_id":"qf-function-graph-point","seed":202610036050,"semantic_template":"qf-function-graph-point/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_point\",\"x\":12}"},"fields":{"title":"Graph Point for a Permitted Input","stem":"In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). Which ordered graph point corresponds to the permitted input 12?","answer":{"kind":"expression","value":"(12, 23)","explanation":"The point is (12, 23). Its first coordinate is the permitted input in D and its second coordinate is the unique output."},"skills":["Graph Point for a Permitted Input"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0051","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b15e00f29074a9839f44d10bb91ac7c16d3fe57c12ccd7a586a8d7ae6cf47dd7","family_id":"qf-function-graph-finite-set","seed":202610036051,"semantic_template":"qf-function-graph-finite-set/{\"A\":[],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D=∅ and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"∅","explanation":"For every input in D, list (x,f(x)). The graph is ∅; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0052","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be8c8881512f7064f26b9ea851dde28d9ff9599c2be20db9fd227eeddc99b103","family_id":"qf-function-graph-finite-set","seed":202610036052,"semantic_template":"qf-function-graph-finite-set/{\"A\":[0],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={0} and f:D→R is given by f(x)=(-1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(0, 0)}","explanation":"For every input in D, list (x,f(x)). The graph is {(0, 0)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0053","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f434d8f12ddf3c6ce8ddd7c9e1ec551673e854afe341442e9bcc4939af8940db","family_id":"qf-function-graph-finite-set","seed":202610036053,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-10,-9,-8],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-10, 1), (-9, 1), (-8, 1)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-10, 1), (-9, 1), (-8, 1)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0054","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ab824c157f8b6eaa54109d7a960b25d15574db4c60e65b10765ac120fc6fd0c","family_id":"qf-function-graph-finite-set","seed":202610036054,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-9,-8,-7],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-9, -7), (-8, -6), (-7, -5)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-9, -7), (-8, -6), (-7, -5)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0055","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"268b32642922f6dc889d15eaf3e227cac19b4555448dfc11234f066dbc032232","family_id":"qf-function-graph-finite-set","seed":202610036055,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-8,-7,-6],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-8, -17), (-7, -15), (-6, -13)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-8, -17), (-7, -15), (-6, -13)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0056","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4e08796a4d41ba1474f73ccc7889466e16f7b0bcbe746c87017d201479e5953","family_id":"qf-function-graph-finite-set","seed":202610036056,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-7,-6,-5],\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-7, 14), (-6, 12), (-5, 10)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-7, 14), (-6, 12), (-5, 10)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0057","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0509b6b75b2e45fff4675df30c988a8a38c1d58decc23023a041122f43f15d5b","family_id":"qf-function-graph-finite-set","seed":202610036057,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-6,-5,-4],\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-6, 7), (-5, 6), (-4, 5)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-6, 7), (-5, 6), (-4, 5)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0058","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e884fe334d4c1d0947bd5f994d2ae0098e5ad03c717ce69d0f8f8af0f18782a3","family_id":"qf-function-graph-finite-set","seed":202610036058,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-5,-4,-3],\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-5, 2), (-4, 2), (-3, 2)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-5, 2), (-4, 2), (-3, 2)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0059","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"677c6b2ae5925db74002f840fce288ff62a866c39f22354a82a7688e1558785d","family_id":"qf-function-graph-finite-set","seed":202610036059,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-4,-3,-2],\"b\":-1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-4, -5), (-3, -4), (-2, -3)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-4, -5), (-3, -4), (-2, -3)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0060","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68929c27ab077b71a55c1df854fcf872dfbcc4839398fd89b148d104a496b117","family_id":"qf-function-graph-finite-set","seed":202610036060,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-3,-2,-1],\"b\":0,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-3, -6), (-2, -4), (-1, -2)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-3, -6), (-2, -4), (-1, -2)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0061","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0bac857cbe74210663bfa4c99614ef4cc42874964898b00aa1eae87b5fb8facd","family_id":"qf-function-graph-finite-set","seed":202610036061,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-2,-1,0],\"b\":1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-2, 5), (-1, 3), (0, 1)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-2, 5), (-1, 3), (0, 1)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0062","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c577cc42dc30e1e8f96faea9e5d47aa52d2426cd9456e8f6485a061266a45aa3","family_id":"qf-function-graph-finite-set","seed":202610036062,"semantic_template":"qf-function-graph-finite-set/{\"A\":[-1,0,1],\"b\":2,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(-1, 3), (0, 2), (1, 1)}","explanation":"For every input in D, list (x,f(x)). The graph is {(-1, 3), (0, 2), (1, 1)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0063","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"daec1da076e3b11a13c3358649d7ef526de274ee12961c7851f13858982f0446","family_id":"qf-function-graph-finite-set","seed":202610036063,"semantic_template":"qf-function-graph-finite-set/{\"A\":[0,1,2],\"b\":-1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(0, -1), (1, -1), (2, -1)}","explanation":"For every input in D, list (x,f(x)). The graph is {(0, -1), (1, -1), (2, -1)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0064","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50403ae6d0db5b53395938080510b0d06ea03c38c6659e712d70cb2a37e8123d","family_id":"qf-function-graph-finite-set","seed":202610036064,"semantic_template":"qf-function-graph-finite-set/{\"A\":[1,2,3],\"b\":0,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(1, 1), (2, 2), (3, 3)}","explanation":"For every input in D, list (x,f(x)). The graph is {(1, 1), (2, 2), (3, 3)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0065","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30aa828f290589d6d0a864841f57bd0fbb0d945a6b0c05b8f866a9b5451b92e7","family_id":"qf-function-graph-finite-set","seed":202610036065,"semantic_template":"qf-function-graph-finite-set/{\"A\":[2,3,4],\"b\":1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(2, 5), (3, 7), (4, 9)}","explanation":"For every input in D, list (x,f(x)). The graph is {(2, 5), (3, 7), (4, 9)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0066","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8495f6033e296a90e405baabd68a142423beb4113ebe6e68fe829b35a155659b","family_id":"qf-function-graph-finite-set","seed":202610036066,"semantic_template":"qf-function-graph-finite-set/{\"A\":[3,4,5],\"b\":2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(3, -4), (4, -6), (5, -8)}","explanation":"For every input in D, list (x,f(x)). The graph is {(3, -4), (4, -6), (5, -8)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0067","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b78a7291901c0211dc94a5079ed902de1300802fded59edfb7c5cbf1e6dbb5a","family_id":"qf-function-graph-finite-set","seed":202610036067,"semantic_template":"qf-function-graph-finite-set/{\"A\":[4,5,6],\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(4, -5), (5, -6), (6, -7)}","explanation":"For every input in D, list (x,f(x)). The graph is {(4, -5), (5, -6), (6, -7)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0068","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90dd3cecbe78a4d72c60a5ab5ae4bbf9bc6c512ab8bcdf8f22cd60551f820926","family_id":"qf-function-graph-finite-set","seed":202610036068,"semantic_template":"qf-function-graph-finite-set/{\"A\":[5,6,7],\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(5, 0), (6, 0), (7, 0)}","explanation":"For every input in D, list (x,f(x)). The graph is {(5, 0), (6, 0), (7, 0)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0069","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78e709c8694e0e14e4659e855e814497004040912b8185f9179e90b1a3b8ca32","family_id":"qf-function-graph-finite-set","seed":202610036069,"semantic_template":"qf-function-graph-finite-set/{\"A\":[6,7,8],\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(6, 7), (7, 8), (8, 9)}","explanation":"For every input in D, list (x,f(x)). The graph is {(6, 7), (7, 8), (8, 9)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0070","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"79bc2782ec2e1599bc9e3e47b813dc9521919129e28bf12a63bfe9ce1acbb821","family_id":"qf-function-graph-finite-set","seed":202610036070,"semantic_template":"qf-function-graph-finite-set/{\"A\":[7,8,9],\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(7, 16), (8, 18), (9, 20)}","explanation":"For every input in D, list (x,f(x)). The graph is {(7, 16), (8, 18), (9, 20)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0071","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e22d84bef083c9261ab52c1ad31cbf5a8a5580113a3854e52581c8e7e73b056","family_id":"qf-function-graph-finite-set","seed":202610036071,"semantic_template":"qf-function-graph-finite-set/{\"A\":[8,9,10],\"b\":-1,\"domain\":\"reals\",\"m\":-2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(8, -17), (9, -19), (10, -21)}","explanation":"For every input in D, list (x,f(x)). The graph is {(8, -17), (9, -19), (10, -21)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0072","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0cdca1deb3216cce1828f4d83b0c44a9c871fc2c26e4229991f20fe51cd1af41","family_id":"qf-function-graph-finite-set","seed":202610036072,"semantic_template":"qf-function-graph-finite-set/{\"A\":[9,10,11],\"b\":0,\"domain\":\"reals\",\"m\":-1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(9, -9), (10, -10), (11, -11)}","explanation":"For every input in D, list (x,f(x)). The graph is {(9, -9), (10, -10), (11, -11)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0073","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e522058275022d52c7ab4d30ffc4ee48decb0406b45d969245ef0dd4f38523c","family_id":"qf-function-graph-finite-set","seed":202610036073,"semantic_template":"qf-function-graph-finite-set/{\"A\":[10,11,12],\"b\":1,\"domain\":\"reals\",\"m\":0,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(10, 1), (11, 1), (12, 1)}","explanation":"For every input in D, list (x,f(x)). The graph is {(10, 1), (11, 1), (12, 1)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0074","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e25e560b486e9223d74d8231b16103f57edde4aef6a44fe3134a5913b468c02","family_id":"qf-function-graph-finite-set","seed":202610036074,"semantic_template":"qf-function-graph-finite-set/{\"A\":[11,12,13],\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(11, 13), (12, 14), (13, 15)}","explanation":"For every input in D, list (x,f(x)). The graph is {(11, 13), (12, 14), (13, 15)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0075","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8eab4610904f78f4d77c50e6229c4693e84b3932cf7b7a7c885820be6477c1c5","family_id":"qf-function-graph-finite-set","seed":202610036075,"semantic_template":"qf-function-graph-finite-set/{\"A\":[12,13,14],\"b\":-1,\"domain\":\"reals\",\"m\":2,\"operation\":\"graph_set\"}"},"fields":{"title":"Listing a Finite Function Graph","stem":"In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.","answer":{"kind":"expression","value":"{(12, 23), (13, 25), (14, 27)}","explanation":"For every input in D, list (x,f(x)). The graph is {(12, 23), (13, 25), (14, 27)}; an empty domain gives the empty graph ∅."},"skills":["Listing a Finite Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0076","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83a4b7dbadb4bc53f6fe3354ef83d2b9237c222d4a1311d022481110cd1ecde6","family_id":"qf-function-graph-table-validity","seed":202610036076,"semantic_template":"qf-function-graph-table-validity/{\"A\":[],\"B\":[],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D=∅ and codomain is B=∅. Is the ordered-pair set ∅ exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"Yes","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0077","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25e203b622687f86202c28acf9d19ee73152dedc4ead9bc3b1d4ed12fb064bc2","family_id":"qf-function-graph-table-validity","seed":202610036077,"semantic_template":"qf-function-graph-table-validity/{\"A\":[-27,-26],\"B\":[-9,-8,-7],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-27,-9]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-27, -26} and codomain is B={-9, -8, -7}. Is the ordered-pair set {(-27, -9)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0078","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbcc6e359ad6ef2a12f56cca07335f2fb45beba1fb0d969b8069c4938c015ae5","family_id":"qf-function-graph-table-validity","seed":202610036078,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-24, -23} and codomain is B={-8, -7, -6}. Is the ordered-pair set {(-24, -8), (-23, -7), (-24, -6)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0079","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5f1f720464072ddcdbb14a86ff3f52102f504f654de05cca352c219322c09e2","family_id":"qf-function-graph-table-validity","seed":202610036079,"semantic_template":"qf-function-graph-table-validity/{\"A\":[-21,-20],\"B\":[-7,-6,-5],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-21,-7],[-20,33]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-21, -20} and codomain is B={-7, -6, -5}. Is the ordered-pair set {(-21, -7), (-20, 33)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0080","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d368d9fb893e253e8c559a1118c91f7bdc27c5d141b8dc07667a5a5b920e2b6b","family_id":"qf-function-graph-table-validity","seed":202610036080,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-18, -17} and codomain is B={-6, -5, -4}. Is the ordered-pair set {(-18, -6), (-17, -5), (-16, -6)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0081","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8094624bfcf87aeafa99223d0bc60ae9268ea4a57e7b6f33b95b82c93a102c25","family_id":"qf-function-graph-table-validity","seed":202610036081,"semantic_template":"qf-function-graph-table-validity/{\"A\":[-15,-14],\"B\":[-5,-4,-3],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-15,-5],[-14,-4]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-15, -14} and codomain is B={-5, -4, -3}. Is the ordered-pair set {(-15, -5), (-14, -4)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"Yes","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0082","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecf044b20e15e6f99486f7de3a8b215d9cbda71dc92a7293f6637aad8c6a7d98","family_id":"qf-function-graph-table-validity","seed":202610036082,"semantic_template":"qf-function-graph-table-validity/{\"A\":[-12,-11],\"B\":[-4,-3,-2],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-12,-4]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-12, -11} and codomain is B={-4, -3, -2}. Is the ordered-pair set {(-12, -4)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0083","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6c54cf753ece37d81f8636c48753f0c6e021d04b91842c7f9c239ab6cf8c8c5f","family_id":"qf-function-graph-table-validity","seed":202610036083,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-9, -8} and codomain is B={-3, -2, -1}. Is the ordered-pair set {(-9, -3), (-8, -2), (-9, -1)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0084","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2bada2acd1f30b6cc71cf4605fc7fba1fea70c1c1cbb224d97f3f8bf47fb857b","family_id":"qf-function-graph-table-validity","seed":202610036084,"semantic_template":"qf-function-graph-table-validity/{\"A\":[-6,-5],\"B\":[-2,-1,0],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[-6,-2],[-5,38]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-6, -5} and codomain is B={-2, -1, 0}. Is the ordered-pair set {(-6, -2), (-5, 38)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0085","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e550d9fd9bb642f193767d87fc54d6ec1caf897baa8d19ba1c3338d2f2bf4d1","family_id":"qf-function-graph-table-validity","seed":202610036085,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={-3, -2} and codomain is B={-1, 0, 1}. Is the ordered-pair set {(-3, -1), (-2, 0), (-1, -1)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0086","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c7fa42480f5010e1271f465f78942ef16491573f3ac482324ed08959e0410f4a","family_id":"qf-function-graph-table-validity","seed":202610036086,"semantic_template":"qf-function-graph-table-validity/{\"A\":[0,1],\"B\":[0,1,2],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[0,0],[1,1]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={0, 1} and codomain is B={0, 1, 2}. Is the ordered-pair set {(0, 0), (1, 1)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"Yes","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0087","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"840f7e88109c64595ad5416f7215a6fea3ed8e62fb4969e265fd6bf1dec0539f","family_id":"qf-function-graph-table-validity","seed":202610036087,"semantic_template":"qf-function-graph-table-validity/{\"A\":[3,4],\"B\":[1,2,3],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[3,1]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={3, 4} and codomain is B={1, 2, 3}. Is the ordered-pair set {(3, 1)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0088","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4b6f535294ee1f88500fa917a7053025a76fc7a33a15afbaeabb99fe6465ca1","family_id":"qf-function-graph-table-validity","seed":202610036088,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={6, 7} and codomain is B={2, 3, 4}. Is the ordered-pair set {(6, 2), (7, 3), (6, 4)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0089","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61fd7ba81f09c323931cb15fc7e1e0899bfd48c6c159aeb4137802c8b68d2e58","family_id":"qf-function-graph-table-validity","seed":202610036089,"semantic_template":"qf-function-graph-table-validity/{\"A\":[9,10],\"B\":[3,4,5],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[9,3],[10,43]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={9, 10} and codomain is B={3, 4, 5}. Is the ordered-pair set {(9, 3), (10, 43)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0090","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c1ee90e96bd30ee046502b1fbcfe9a49c47d6e94186bb364280063adfb370bd","family_id":"qf-function-graph-table-validity","seed":202610036090,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={12, 13} and codomain is B={4, 5, 6}. Is the ordered-pair set {(12, 4), (13, 5), (14, 4)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0091","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"778a9b9966bae1a9ebf25e5ebfdff12d9bd613cecc205cb9878a08f70bb523f6","family_id":"qf-function-graph-table-validity","seed":202610036091,"semantic_template":"qf-function-graph-table-validity/{\"A\":[15,16],\"B\":[5,6,7],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[15,5],[16,6]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={15, 16} and codomain is B={5, 6, 7}. Is the ordered-pair set {(15, 5), (16, 6)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"Yes","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0092","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36ef24bb9ca78444b7ce1fd52c176d92e79370dfc0b6da195ebe345b8fb97f94","family_id":"qf-function-graph-table-validity","seed":202610036092,"semantic_template":"qf-function-graph-table-validity/{\"A\":[18,19],\"B\":[6,7,8],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[18,6]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={18, 19} and codomain is B={6, 7, 8}. Is the ordered-pair set {(18, 6)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0093","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd15bfe7afd0bc98fa03b66b5eaf7c6a27b12ebd9744c02a392d79ebcd33e836","family_id":"qf-function-graph-table-validity","seed":202610036093,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={21, 22} and codomain is B={7, 8, 9}. Is the ordered-pair set {(21, 7), (22, 8), (21, 9)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0094","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d4fc0cad72f34e91594819cba96cdfc7cc7d772ca9f5fd0175cd29851454cdd","family_id":"qf-function-graph-table-validity","seed":202610036094,"semantic_template":"qf-function-graph-table-validity/{\"A\":[24,25],\"B\":[8,9,10],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[24,8],[25,48]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={24, 25} and codomain is B={8, 9, 10}. Is the ordered-pair set {(24, 8), (25, 48)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0095","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ee5e664a7b1cbbccb625a1acb9f122381ded2953a5a1e29a25c7db1c555aae4","family_id":"qf-function-graph-table-validity","seed":202610036095,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={27, 28} and codomain is B={9, 10, 11}. Is the ordered-pair set {(27, 9), (28, 10), (29, 9)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0096","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e5dc99dc3741de4494808ed257e34946f1524c535e4891b5f383f386c0f652f","family_id":"qf-function-graph-table-validity","seed":202610036096,"semantic_template":"qf-function-graph-table-validity/{\"A\":[30,31],\"B\":[10,11,12],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[30,10],[31,11]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={30, 31} and codomain is B={10, 11, 12}. Is the ordered-pair set {(30, 10), (31, 11)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"Yes","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0097","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18412157da589d416ceda544deee44878e68a9b4900fd112a7a6c83f1d6c7f27","family_id":"qf-function-graph-table-validity","seed":202610036097,"semantic_template":"qf-function-graph-table-validity/{\"A\":[33,34],\"B\":[11,12,13],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[33,11]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={33, 34} and codomain is B={11, 12, 13}. Is the ordered-pair set {(33, 11)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0098","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cab08f4101e2b695d6f3e206062828048ca6d61c1dd865f544691e8ba5cde9e","family_id":"qf-function-graph-table-validity","seed":202610036098,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={36, 37} and codomain is B={12, 13, 14}. Is the ordered-pair set {(36, 12), (37, 13), (36, 14)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0099","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cfde61bdadf517cc963547229980b556bcad23f7204df476af9ab5606b2d5799","family_id":"qf-function-graph-table-validity","seed":202610036099,"semantic_template":"qf-function-graph-table-validity/{\"A\":[39,40],\"B\":[13,14,15],\"domain\":\"reals\",\"operation\":\"graph_validity\",\"pairs\":[[39,13],[40,53]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={39, 40} and codomain is B={13, 14, 15}. Is the ordered-pair set {(39, 13), (40, 53)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r06-function-graph-0100","batch_id":"batch-20261003-r06-function-graph-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d50d31302ba5253d9c3310da69414a9674d1f085586181a7d47df7351387368","family_id":"qf-function-graph-table-validity","seed":202610036100,"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]]}"},"fields":{"title":"Validity of a Finite Total-Function Graph","stem":"The declared domain is D={42, 43} and codomain is B={14, 15, 16}. Is the ordered-pair set {(42, 14), (43, 15), (44, 14)} exactly the graph of a total function D→B?","answer":{"kind":"short_text","value":"No","explanation":"Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D."},"skills":["Validity of a Finite Total-Function Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}