{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261003-r05-linear-function-0001","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81ed0d26469e3414e77bad32b63383c60974f292fb7d34bcb435bb82274b268f","family_id":"qf-affine-exact-evaluation","seed":202610035001,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":-12,\"operation\":\"affine_evaluate\",\"x\":-4}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-12)x+(-3). Compute f(-4) exactly.","answer":{"kind":"numeric","value":"45","explanation":"Multiply the input by the slope, then add the intercept: f(-4)=45. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0002","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88184739d386980521af9bd11394ef529e11f2fe17a35a2bea7cb7622e370053","family_id":"qf-affine-exact-evaluation","seed":202610035002,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":-11,\"operation\":\"affine_evaluate\",\"x\":-3}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-11)x+(-2). Compute f(-3) exactly.","answer":{"kind":"numeric","value":"31","explanation":"Multiply the input by the slope, then add the intercept: f(-3)=31. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0003","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c676a6de0ebbf4affadb06049ba7159bddf117620523dae80dae3202447d224f","family_id":"qf-affine-exact-evaluation","seed":202610035003,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":-10,\"operation\":\"affine_evaluate\",\"x\":-2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-10)x+(-1). Compute f(-2) exactly.","answer":{"kind":"numeric","value":"19","explanation":"Multiply the input by the slope, then add the intercept: f(-2)=19. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0004","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"883a00615ca0c5513573cb6df1979d542b1fd201f9eaf5a1be888f71b3c73d24","family_id":"qf-affine-exact-evaluation","seed":202610035004,"semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":-9,\"operation\":\"affine_evaluate\",\"x\":-1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-9)x+(0). Compute f(-1) exactly.","answer":{"kind":"numeric","value":"9","explanation":"Multiply the input by the slope, then add the intercept: f(-1)=9. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0005","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63bdfdb5186d155490e46e9a59e402b56dd8e5c35e560aeb2ef81fc95c91c8df","family_id":"qf-affine-exact-evaluation","seed":202610035005,"semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":-8,\"operation\":\"affine_evaluate\",\"x\":0}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-8)x+(1). Compute f(0) exactly.","answer":{"kind":"numeric","value":"1","explanation":"Multiply the input by the slope, then add the intercept: f(0)=1. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0006","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd2f661fd914322494b5b5f847703fa9aac5e2bafcd39df06ab038d05a04409d","family_id":"qf-affine-exact-evaluation","seed":202610035006,"semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"affine_evaluate\",\"x\":1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-7)x+(2). Compute f(1) exactly.","answer":{"kind":"numeric","value":"-5","explanation":"Multiply the input by the slope, then add the intercept: f(1)=-5. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0007","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab65696b015cf2f01c35b7c2581176e9aa082e8d5a5aabff88eb80da9b30c867","family_id":"qf-affine-exact-evaluation","seed":202610035007,"semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":-6,\"operation\":\"affine_evaluate\",\"x\":2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-6)x+(3). Compute f(2) exactly.","answer":{"kind":"numeric","value":"-9","explanation":"Multiply the input by the slope, then add the intercept: f(2)=-9. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0008","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a59c0d9ee2a2fb537e98fc1152d4b9289e1da38d67d975bb921fb78f1a031f12","family_id":"qf-affine-exact-evaluation","seed":202610035008,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":-5,\"operation\":\"affine_evaluate\",\"x\":3}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-5)x+(-3). Compute f(3) exactly.","answer":{"kind":"numeric","value":"-18","explanation":"Multiply the input by the slope, then add the intercept: f(3)=-18. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0009","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45bd6fe357cf8f1e1679096a5b9a2efc059f7a1cd02b38c31be239d7aa65b955","family_id":"qf-affine-exact-evaluation","seed":202610035009,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":-4,\"operation\":\"affine_evaluate\",\"x\":4}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-4)x+(-2). Compute f(4) exactly.","answer":{"kind":"numeric","value":"-18","explanation":"Multiply the input by the slope, then add the intercept: f(4)=-18. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0010","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e284a2cf030813bedfef402ed356ef6b59a4f23c3d08b990fd82cda583fb6483","family_id":"qf-affine-exact-evaluation","seed":202610035010,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":-3,\"operation\":\"affine_evaluate\",\"x\":-4}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-3)x+(-1). Compute f(-4) exactly.","answer":{"kind":"numeric","value":"11","explanation":"Multiply the input by the slope, then add the intercept: f(-4)=11. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0011","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"615833c56594b921c428595fa6464cf3e2508d00dee34d02ebe46380937f8ab3","family_id":"qf-affine-exact-evaluation","seed":202610035011,"semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"affine_evaluate\",\"x\":-3}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-2)x+(0). Compute f(-3) exactly.","answer":{"kind":"numeric","value":"6","explanation":"Multiply the input by the slope, then add the intercept: f(-3)=6. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0012","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5b58436c750e14aa6b83ae7a564eebe1417658de661b2798d684059b81866b2","family_id":"qf-affine-exact-evaluation","seed":202610035012,"semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"affine_evaluate\",\"x\":-2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(-1)x+(1). Compute f(-2) exactly.","answer":{"kind":"numeric","value":"3","explanation":"Multiply the input by the slope, then add the intercept: f(-2)=3. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0013","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03211e5f0f5f41dfd7c18f2912388815d431452a182711fbf477bc17ccc6650e","family_id":"qf-affine-exact-evaluation","seed":202610035013,"semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"affine_evaluate\",\"x\":-1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(0)x+(2). Compute f(-1) exactly.","answer":{"kind":"numeric","value":"2","explanation":"Multiply the input by the slope, then add the intercept: f(-1)=2. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0014","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bea7d89236a4b859424edf569972fe03fc2a2f66f51802b96b88ec05f5650afe","family_id":"qf-affine-exact-evaluation","seed":202610035014,"semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":1,\"operation\":\"affine_evaluate\",\"x\":0}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(1)x+(3). Compute f(0) exactly.","answer":{"kind":"numeric","value":"3","explanation":"Multiply the input by the slope, then add the intercept: f(0)=3. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0015","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de9090d856885d9987fef16d2c07e065734d7137dc519ff997cb57498791ce98","family_id":"qf-affine-exact-evaluation","seed":202610035015,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":2,\"operation\":\"affine_evaluate\",\"x\":1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(2)x+(-3). Compute f(1) exactly.","answer":{"kind":"numeric","value":"-1","explanation":"Multiply the input by the slope, then add the intercept: f(1)=-1. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0016","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9dad3ca9ac0f2bf0a3aed718a43af9e28ee617a8423b7eaea0c9ef86a3adfa84","family_id":"qf-affine-exact-evaluation","seed":202610035016,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"affine_evaluate\",\"x\":2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(3)x+(-2). Compute f(2) exactly.","answer":{"kind":"numeric","value":"4","explanation":"Multiply the input by the slope, then add the intercept: f(2)=4. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0017","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31b535b921e5f2df3be9763e805a6fa91787daacec3365281f845085b13288d8","family_id":"qf-affine-exact-evaluation","seed":202610035017,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"affine_evaluate\",\"x\":3}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(4)x+(-1). Compute f(3) exactly.","answer":{"kind":"numeric","value":"11","explanation":"Multiply the input by the slope, then add the intercept: f(3)=11. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0018","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4a030d7dc7f66c39cdaed51c9ee81dcf38d42524f3c8eeb2c2582e636555af4","family_id":"qf-affine-exact-evaluation","seed":202610035018,"semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"affine_evaluate\",\"x\":4}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(5)x+(0). Compute f(4) exactly.","answer":{"kind":"numeric","value":"20","explanation":"Multiply the input by the slope, then add the intercept: f(4)=20. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0019","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3737222fd4fe76a1418d36e55524a0c86e3881b3c254f56c823b7fdd2341a4b2","family_id":"qf-affine-exact-evaluation","seed":202610035019,"semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"affine_evaluate\",\"x\":-4}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(6)x+(1). Compute f(-4) exactly.","answer":{"kind":"numeric","value":"-23","explanation":"Multiply the input by the slope, then add the intercept: f(-4)=-23. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0020","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a9ef26537467bba363373031cf9d39614037521b1bccf0bcb0d8fadaa0b9370","family_id":"qf-affine-exact-evaluation","seed":202610035020,"semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"affine_evaluate\",\"x\":-3}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(7)x+(2). Compute f(-3) exactly.","answer":{"kind":"numeric","value":"-19","explanation":"Multiply the input by the slope, then add the intercept: f(-3)=-19. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0021","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7451e9e4f13b9ba05195e3c70016b3dd0716fd0f670f78e1f53322f9d05f3aa","family_id":"qf-affine-exact-evaluation","seed":202610035021,"semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":8,\"operation\":\"affine_evaluate\",\"x\":-2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(8)x+(3). Compute f(-2) exactly.","answer":{"kind":"numeric","value":"-13","explanation":"Multiply the input by the slope, then add the intercept: f(-2)=-13. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0022","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c86f950e32660c255728442197b13f449380b6563b4e98d17f392bf6a8a0bf7a","family_id":"qf-affine-exact-evaluation","seed":202610035022,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":9,\"operation\":\"affine_evaluate\",\"x\":-1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(9)x+(-3). Compute f(-1) exactly.","answer":{"kind":"numeric","value":"-12","explanation":"Multiply the input by the slope, then add the intercept: f(-1)=-12. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0023","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a16b8dab549172db8fc97bd473d78ca8a16db8a027f1e954bb6692982642c3f0","family_id":"qf-affine-exact-evaluation","seed":202610035023,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":10,\"operation\":\"affine_evaluate\",\"x\":0}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(10)x+(-2). Compute f(0) exactly.","answer":{"kind":"numeric","value":"-2","explanation":"Multiply the input by the slope, then add the intercept: f(0)=-2. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0024","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77f19afe8919f2cdc81ff19c4d9c88b2f3bd8d49346c8cfc5337ff34eef29c3d","family_id":"qf-affine-exact-evaluation","seed":202610035024,"semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":11,\"operation\":\"affine_evaluate\",\"x\":1}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(11)x+(-1). Compute f(1) exactly.","answer":{"kind":"numeric","value":"10","explanation":"Multiply the input by the slope, then add the intercept: f(1)=10. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0025","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c058c932629330be760f69be4e582a94f9dc0eff5a7dfa60659530fbc4a1d2d7","family_id":"qf-affine-exact-evaluation","seed":202610035025,"semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":12,\"operation\":\"affine_evaluate\",\"x\":2}"},"fields":{"title":"Exact Affine-Function Evaluation","stem":"Over R, f(x)=(12)x+(0). Compute f(2) exactly.","answer":{"kind":"numeric","value":"24","explanation":"Multiply the input by the slope, then add the intercept: f(2)=24. Constant functions with m=0 also belong to the affine family."},"skills":["Exact Affine-Function Evaluation"],"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-r05-linear-function-0026","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd1f79d46e078c33ff592b0025c96466fb8d9144d6697c12e27d0ac7564159d6","family_id":"qf-affine-two-point-slope","seed":202610035026,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-12,\"x2\":-11,\"y1\":-2,\"y2\":-14}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-12, -2) and (-11, -14), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-12/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -12/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0027","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd1058926b25f1ba569a00a661a3346e070bb85cd5a6e6ad6a78f3c4d7485b4f","family_id":"qf-affine-two-point-slope","seed":202610035027,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-11,\"y1\":-12,\"y2\":-1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-11, -1) and (-13, -12), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"11/2","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 11/2. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0028","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29cb983d8d6f9897945291849e0bc1d3e9e1dfc0dc3b386c60338d2afb16c130","family_id":"qf-affine-two-point-slope","seed":202610035028,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-10,\"x2\":-7,\"y1\":0,\"y2\":-10}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-10, 0) and (-7, -10), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-10/3","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -10/3. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0029","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e12f2437279ec3eb8451a66659158f6767de60e08ff55ccae59770e98316d0d","family_id":"qf-affine-two-point-slope","seed":202610035029,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-9,\"y1\":-8,\"y2\":1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-9, 1) and (-13, -8), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"9/4","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 9/4. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0030","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bce3f8cdf1b41ba711886ffe38140322f951bc57a5bc3e24bb9483aaf90c1e50","family_id":"qf-affine-two-point-slope","seed":202610035030,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-8,\"x2\":-3,\"y1\":2,\"y2\":-6}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-8, 2) and (-3, -6), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-8/5","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -8/5. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0031","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf56948781c4add39e32ab15bc8912cdb25c86b9f5cbcecb874556149aa12ccd","family_id":"qf-affine-two-point-slope","seed":202610035031,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-7,\"y1\":-9,\"y2\":-2}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-7, -2) and (-13, -9), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"7/6","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 7/6. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0032","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c90e789ee1bccc4178ca8497fb0ba1ca8964ae184940f264fdfffc3d35dc0bd5","family_id":"qf-affine-two-point-slope","seed":202610035032,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-6,\"x2\":-5,\"y1\":-1,\"y2\":-7}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-6, -1) and (-5, -7), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-6/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -6/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0033","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd1084ca6d54bb87628b3ad6e3e7c376c85958bb83b0cd2448bd1f3ccc0f161a","family_id":"qf-affine-two-point-slope","seed":202610035033,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-5,\"y1\":-5,\"y2\":0}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-5, 0) and (-7, -5), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"5/2","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 5/2. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0034","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"efb664612816ebe723f2868aa059473569e35809b044a72653332e5f963e55cc","family_id":"qf-affine-two-point-slope","seed":202610035034,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-4,\"x2\":-1,\"y1\":1,\"y2\":-3}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-4, 1) and (-1, -3), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-4/3","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -4/3. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0035","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d21e7a96957b7463403b78824796629e4b012ca20627886153009b7de039d741","family_id":"qf-affine-two-point-slope","seed":202610035035,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-3,\"y1\":-1,\"y2\":2}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-3, 2) and (-7, -1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"3/4","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 3/4. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0036","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"374638d8cd14303f6b0d352b9cef39ed81ae48c70d242be7b7ac6a498114bf25","family_id":"qf-affine-two-point-slope","seed":202610035036,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-2,\"x2\":3,\"y1\":-2,\"y2\":-4}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-2, -2) and (3, -4), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-2/5","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -2/5. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0037","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a8c68b61fdf71b94473ed5aa6ba1235ac6e385d150fd5a57d178d7430cd15c49","family_id":"qf-affine-two-point-slope","seed":202610035037,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-1,\"y1\":-2,\"y2\":-1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (-1, -1) and (-7, -2), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"1/6","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 1/6. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0038","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee66b1ada51a93dd31405c8ec5cd683ef09522439176af9a37042d1eee927071","family_id":"qf-affine-two-point-slope","seed":202610035038,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":0,\"x2\":1,\"y1\":0,\"y2\":0}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (0, 0) and (1, 0), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"0/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 0/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0039","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f0d24f34a37113a357439c22051147c277696ff0d5fcf48043d99b5f440d7b4","family_id":"qf-affine-two-point-slope","seed":202610035039,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":1,\"y1\":2,\"y2\":1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (1, 1) and (-1, 2), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-1/2","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -1/2. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0040","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bceebaaf53a48e2c9cbd79a32b84dfde45eaa6b90ded30187b3f8cadb81777b5","family_id":"qf-affine-two-point-slope","seed":202610035040,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":2,\"x2\":5,\"y1\":2,\"y2\":4}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (2, 2) and (5, 4), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"2/3","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 2/3. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0041","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5a3beac276f850e067e5fa1fa378887f693e4f27cb1ed37df4efa0c7a176fa9","family_id":"qf-affine-two-point-slope","seed":202610035041,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":3,\"y1\":1,\"y2\":-2}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (3, -2) and (-1, 1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-3/4","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -3/4. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0042","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b34ee7f3e7ba907359f73bd6742d32b122a57e2e61b3fc14ff6054a9f938f6d5","family_id":"qf-affine-two-point-slope","seed":202610035042,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":4,\"x2\":9,\"y1\":-1,\"y2\":3}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (4, -1) and (9, 3), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"4/5","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 4/5. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0043","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3cd57773a553088d85d2204c353f54307aba6a2e4ba687aec38e78a44bbf4e03","family_id":"qf-affine-two-point-slope","seed":202610035043,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":5,\"y1\":5,\"y2\":0}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (5, 0) and (-1, 5), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-5/6","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -5/6. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0044","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecea1a63b5b0b02de5921866980d2160bb4f5eb799f760ecf0bac0547b53e4f9","family_id":"qf-affine-two-point-slope","seed":202610035044,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":6,\"x2\":7,\"y1\":1,\"y2\":7}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (6, 1) and (7, 7), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"6/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 6/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0045","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bdc7902e7189d73bb82bf2ef4c7d375ff28868ebd37305f85e24d697dea5222","family_id":"qf-affine-two-point-slope","seed":202610035045,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":7,\"y1\":9,\"y2\":2}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (7, 2) and (5, 9), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-7/2","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -7/2. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0046","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea1a3a66e2a09c26ddeb857e73b3167b7b92a5dd85d491252688837b3ad4e8d5","family_id":"qf-affine-two-point-slope","seed":202610035046,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":8,\"x2\":11,\"y1\":-2,\"y2\":6}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (8, -2) and (11, 6), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"8/3","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 8/3. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0047","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5fc1133a6f833674ce671cd0e88d251223f8d766e083fd11a3e1b0167c365970","family_id":"qf-affine-two-point-slope","seed":202610035047,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":9,\"y1\":8,\"y2\":-1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (9, -1) and (5, 8), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-9/4","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -9/4. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0048","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4222edcc82272e2c373a5fb3d3194a014f7259287077edeb62b018727331cf5d","family_id":"qf-affine-two-point-slope","seed":202610035048,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":10,\"x2\":15,\"y1\":0,\"y2\":10}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (10, 0) and (15, 10), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"2/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 2/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0049","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d29ff7bb0eb40ec19864bc22c765d22abc7cf5188b627338dcfb8240b9e4832","family_id":"qf-affine-two-point-slope","seed":202610035049,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":11,\"y1\":12,\"y2\":1}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (11, 1) and (5, 12), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"-11/6","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain -11/6. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0050","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e0c142151142e45c11a89b3c3cbf92a6940f5c32b87a9354c28d97931d98e84","family_id":"qf-affine-two-point-slope","seed":202610035050,"semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":12,\"x2\":13,\"y1\":2,\"y2\":14}"},"fields":{"title":"Two-Point Slope of an Affine Graph","stem":"Over the reals, an affine-function graph contains (12, 2) and (13, 14), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.","answer":{"kind":"expression","value":"12/1","explanation":"Use (y_2−y_1)/(x_2−x_1) to obtain 12/1. The denominator is nonzero; this formula does not give the slope of a vertical line."},"skills":["Two-Point Slope of an Affine 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-r05-linear-function-0051","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"548eb0ee8e1d30c7518251d561cf185db6ff334208f5976d048fd0163b105195","family_id":"qf-affine-zero-set","seed":202610035051,"semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(0)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"R","explanation":"The zero set is R. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0052","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe89929a52bb95401c9c9c3edefa4f95420ba3a55dcd6141c6048bfeeccee2d1","family_id":"qf-affine-zero-set","seed":202610035052,"semantic_template":"qf-affine-zero-set/{\"b\":3,\"domain\":\"reals\",\"m\":0,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(0)x+(3). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"∅","explanation":"The zero set is ∅. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0053","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12eec0e5037ad798b7683ccc28d96223bbb2c973bceccbbbe134ea1bb2240b60","family_id":"qf-affine-zero-set","seed":202610035053,"semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":-10,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-10)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{0/1}","explanation":"The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0054","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18f26734960b57cdde1cbc01796daacf1305c4bb0f419269a44e8f2fce1fb84d","family_id":"qf-affine-zero-set","seed":202610035054,"semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":-9,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-9)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/9}","explanation":"The zero set is {1/9}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0055","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ec64b8b4d70a0c4c6484c40acf9f62367642d89860e32d6cd206ad81f393618","family_id":"qf-affine-zero-set","seed":202610035055,"semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":-8,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-8)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/4}","explanation":"The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0056","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1a7420459abf94ba1fa5976e76c6dc34e96408090014f0a623d4f4de81a7b2d","family_id":"qf-affine-zero-set","seed":202610035056,"semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-7)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-2/7}","explanation":"The zero set is {-2/7}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0057","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc36c6c4adaee0ee4bb8d4ba069b5c4c746a1b2fa184633538992f88aec88afa","family_id":"qf-affine-zero-set","seed":202610035057,"semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":-6,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-6)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/6}","explanation":"The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0058","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c6c4aaaa96592303920d776e9898e057163948ac7c46644b5a5b55aa955c858","family_id":"qf-affine-zero-set","seed":202610035058,"semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":-5,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-5)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{0/1}","explanation":"The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0059","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b06405d532c5d367fe9758d72d42ae9d53eec2a0b046f023c0211a131c9c973","family_id":"qf-affine-zero-set","seed":202610035059,"semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":-4,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-4)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/4}","explanation":"The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0060","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a13db5a81c1356c0d4291daec20665883803fab391b51743d59d6c0007e7b9cc","family_id":"qf-affine-zero-set","seed":202610035060,"semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":-3,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-3)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{2/3}","explanation":"The zero set is {2/3}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0061","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32eaa5917f544a690fc9b4653805f1ad5bc3a030b5b3b72541e125747793df4c","family_id":"qf-affine-zero-set","seed":202610035061,"semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-2)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/1}","explanation":"The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0062","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"037386679500755148c0e32b040579fa275720b203ec58885e909c2197a85bbb","family_id":"qf-affine-zero-set","seed":202610035062,"semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(-1)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/1}","explanation":"The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0063","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca6eeeda5ee697fea09824bef3960d8b0e49fadc7d16666d5e882d021f25cb0c","family_id":"qf-affine-zero-set","seed":202610035063,"semantic_template":"qf-affine-zero-set/{\"b\":4,\"domain\":\"reals\",\"m\":1,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(1)x+(4). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-4/1}","explanation":"The zero set is {-4/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0064","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1497fd4dc7bafcf14dc03b2ac36d4839c189a793b581089d8dd19d96266da69","family_id":"qf-affine-zero-set","seed":202610035064,"semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(1)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/1}","explanation":"The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0065","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4fa89d274588099679ed2235febf05588156b93b2eb41d79bbdeb82fb3d811b","family_id":"qf-affine-zero-set","seed":202610035065,"semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(2)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/1}","explanation":"The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0066","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"392c242e7b79b73194637f93b1952c6df44225891c233cb9a7ea7a907edb9c7e","family_id":"qf-affine-zero-set","seed":202610035066,"semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(3)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{2/3}","explanation":"The zero set is {2/3}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0067","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e0ca3008e5c1efb62bcb1127659f471e989bda908caea5617b43f39daf28b78","family_id":"qf-affine-zero-set","seed":202610035067,"semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(4)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/4}","explanation":"The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0068","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bac0e07822d72f32e610ecbff105a00375ddd04e50065655931321ed94422b4f","family_id":"qf-affine-zero-set","seed":202610035068,"semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(5)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{0/1}","explanation":"The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0069","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"773c50dcd581dd7c6dd3ccb30494b60cf6108a92f44ce3d90d808f1c5714f1be","family_id":"qf-affine-zero-set","seed":202610035069,"semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(6)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/6}","explanation":"The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0070","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0a4017bd7350a1b2180f56a36214c371cd5d1578d2e9d1393f7167856bc50e8","family_id":"qf-affine-zero-set","seed":202610035070,"semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(7)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-2/7}","explanation":"The zero set is {-2/7}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0071","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"404716f6c20670ae06684e527b820db33be1d54ed267641b1b03c49f3fdd4e05","family_id":"qf-affine-zero-set","seed":202610035071,"semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":8,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(8)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/4}","explanation":"The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0072","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92e11685b2d63ca973b8822e0f3a7bbb1f424bf24641cdb17afc9d4c5d12ff83","family_id":"qf-affine-zero-set","seed":202610035072,"semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":9,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(9)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{1/9}","explanation":"The zero set is {1/9}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0073","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a8991d4f3ece7e4b9833ffb5a2e000416ca47ddf5cf4cad0a14427601f5a80b","family_id":"qf-affine-zero-set","seed":202610035073,"semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":10,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(10)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{0/1}","explanation":"The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0074","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7649ef3e669b7fe3d4c7764c9a2778c5881af19d93fbf394dc043e12d9b87b98","family_id":"qf-affine-zero-set","seed":202610035074,"semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":11,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(11)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/11}","explanation":"The zero set is {-1/11}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0075","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55dc797cd7373b87c70c8aa8651a413d1baf8d866eb0ceca9944b60885bb8f60","family_id":"qf-affine-zero-set","seed":202610035075,"semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":12,\"operation\":\"zero_set\"}"},"fields":{"title":"Complete Zero Set of an Affine Function","stem":"Over R, f(x)=(12)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.","answer":{"kind":"expression","value":"{-1/6}","explanation":"The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none."},"skills":["Complete Zero Set of an Affine Function"],"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-r05-linear-function-0076","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"376948f2492dd57a7c67e5c6be33d46ea622cd4ac1d7227c488a0784b75f6bb2","family_id":"qf-affine-pointwise-comparison","seed":202610035076,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"compare_at_input\",\"u\":1,\"v\":2,\"x\":0}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(1)x+(2) and g(x)=(1)x+(2). At the single input x=0, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(0)=2 and g(0)=2, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0077","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5119f661c1412cebc2fc14d697cef19012298df5c414c91de49807087ca876da","family_id":"qf-affine-pointwise-comparison","seed":202610035077,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-11,\"operation\":\"compare_at_input\",\"u\":-10,\"v\":2,\"x\":-2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-11)x+(-1) and g(x)=(-10)x+(2). At the single input x=-2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-2)=21 and g(-2)=22, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0078","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7d96b01152bc05843015dd51a346f8897cc488f3ac93681538dcf62eb2b25e5","family_id":"qf-affine-pointwise-comparison","seed":202610035078,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":-10,\"operation\":\"compare_at_input\",\"u\":-9,\"v\":1,\"x\":-1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-10)x+(0) and g(x)=(-9)x+(1). At the single input x=-1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(-1)=10 and g(-1)=10, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0079","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61916bac1a9d2671177882498b5708ffe1d118298880c50e3dead880152dc0fb","family_id":"qf-affine-pointwise-comparison","seed":202610035079,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":-9,\"operation\":\"compare_at_input\",\"u\":-8,\"v\":2,\"x\":0}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-9)x+(1) and g(x)=(-8)x+(2). At the single input x=0, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(0)=1 and g(0)=2, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0080","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1f60097b89116736130cfd4bd568f31a0223387b75431680466681d483a49b3","family_id":"qf-affine-pointwise-comparison","seed":202610035080,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":-8,\"operation\":\"compare_at_input\",\"u\":-7,\"v\":1,\"x\":1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-8)x+(2) and g(x)=(-7)x+(1). At the single input x=1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(1)=-6 and g(1)=-6, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0081","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac5d59eacadb7a4eb2303c65b28b829214c47357bef5f5c41469126a53d9bad6","family_id":"qf-affine-pointwise-comparison","seed":202610035081,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"compare_at_input\",\"u\":-6,\"v\":-3,\"x\":2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-7)x+(-2) and g(x)=(-6)x+(-3). At the single input x=2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(2)=-16 and g(2)=-15, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0082","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b13c387b4056678224ff6dd1fbcfc72f5f76d304cbccc12f6c9c6e29e142624","family_id":"qf-affine-pointwise-comparison","seed":202610035082,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-6,\"operation\":\"compare_at_input\",\"u\":-5,\"v\":-4,\"x\":3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-6)x+(-1) and g(x)=(-5)x+(-4). At the single input x=3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(3)=-19 and g(3)=-19, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0083","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"406c89198e97c8448ae17f146aacebb49a39d93d17fcd1fbf9663dd93a17513d","family_id":"qf-affine-pointwise-comparison","seed":202610035083,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":-5,\"operation\":\"compare_at_input\",\"u\":-4,\"v\":4,\"x\":-3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-5)x+(0) and g(x)=(-4)x+(4). At the single input x=-3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-3)=15 and g(-3)=16, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0084","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce5ace13532f09dad6d16b97958c892f5f6299dd4ada689ea9f8b60f93cd5acc","family_id":"qf-affine-pointwise-comparison","seed":202610035084,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":-4,\"operation\":\"compare_at_input\",\"u\":-3,\"v\":3,\"x\":-2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-4)x+(1) and g(x)=(-3)x+(3). At the single input x=-2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(-2)=9 and g(-2)=9, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0085","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9ce7dff5eaec207eee1c825a9aa8d4a4650d186a392837d7d8b1e3c499b99a9","family_id":"qf-affine-pointwise-comparison","seed":202610035085,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":-3,\"operation\":\"compare_at_input\",\"u\":-2,\"v\":4,\"x\":-1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-3)x+(2) and g(x)=(-2)x+(4). At the single input x=-1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-1)=5 and g(-1)=6, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0086","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f1ba1c350b55893086e91d9d68ef97fd90c1765fc2584aa9623607c4d8bd2881","family_id":"qf-affine-pointwise-comparison","seed":202610035086,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"compare_at_input\",\"u\":-1,\"v\":-2,\"x\":0}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-2)x+(-2) and g(x)=(-1)x+(-2). At the single input x=0, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(0)=-2 and g(0)=-2, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0087","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65de7b72bcbea6d1d5feaa70a492b893035a0afe3fab602cea09e3845cd7338c","family_id":"qf-affine-pointwise-comparison","seed":202610035087,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"compare_at_input\",\"u\":0,\"v\":-1,\"x\":1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(-1)x+(-1) and g(x)=(0)x+(-1). At the single input x=1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(1)=-2 and g(1)=-1, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0088","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6073cccd50f0023d7229fc77fe9299d6ecf27c234c5de09d048a0edaf84853b0","family_id":"qf-affine-pointwise-comparison","seed":202610035088,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"compare_at_input\",\"u\":1,\"v\":-2,\"x\":2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(0)x+(0) and g(x)=(1)x+(-2). At the single input x=2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(2)=0 and g(2)=0, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0089","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2524e0dc110d4ac4d123197262b03e22694a9496244e685f18c8b0729a796f6e","family_id":"qf-affine-pointwise-comparison","seed":202610035089,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"compare_at_input\",\"u\":2,\"v\":-1,\"x\":3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(1)x+(1) and g(x)=(2)x+(-1). At the single input x=3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(3)=4 and g(3)=5, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0090","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2bc119b2fd454b490a4626ea7b998799d11aada58bef6fe1a15ec496811123a6","family_id":"qf-affine-pointwise-comparison","seed":202610035090,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"compare_at_input\",\"u\":3,\"v\":5,\"x\":-3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(2)x+(2) and g(x)=(3)x+(5). At the single input x=-3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(-3)=-4 and g(-3)=-4, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0091","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09ad6f3452371040961ceddc4ad9b685aac1b14917c808a677a1b314fdc2b929","family_id":"qf-affine-pointwise-comparison","seed":202610035091,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"compare_at_input\",\"u\":4,\"v\":1,\"x\":-2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(3)x+(-2) and g(x)=(4)x+(1). At the single input x=-2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-2)=-8 and g(-2)=-7, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0092","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"454e8aa2ae35edaac7c67978473785211a60b69a561bd0ebc801a2607f53bb84","family_id":"qf-affine-pointwise-comparison","seed":202610035092,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"compare_at_input\",\"u\":5,\"v\":0,\"x\":-1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(4)x+(-1) and g(x)=(5)x+(0). At the single input x=-1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(-1)=-5 and g(-1)=-5, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0093","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d1904d31b6017f5aef2d9b20cb48a892e8b67857cd47010e2d64365cbfba9d6","family_id":"qf-affine-pointwise-comparison","seed":202610035093,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"compare_at_input\",\"u\":6,\"v\":1,\"x\":0}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(5)x+(0) and g(x)=(6)x+(1). At the single input x=0, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(0)=0 and g(0)=1, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0094","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9fb85eb40dfd39fbfa2740f9820f41fbb8b57d375e87949fd1c5e772a2757671","family_id":"qf-affine-pointwise-comparison","seed":202610035094,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"compare_at_input\",\"u\":7,\"v\":0,\"x\":1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(6)x+(1) and g(x)=(7)x+(0). At the single input x=1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(1)=7 and g(1)=7, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0095","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e87c82f45aa12f1bc5b65825102b255667aab7adcf43e5049f028ec81720eb6","family_id":"qf-affine-pointwise-comparison","seed":202610035095,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"compare_at_input\",\"u\":8,\"v\":1,\"x\":2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(7)x+(2) and g(x)=(8)x+(1). At the single input x=2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(2)=16 and g(2)=17, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0096","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec9e31a597d81155dec78c3f651e292c0335a0bace59e41625f8045eb0b018ce","family_id":"qf-affine-pointwise-comparison","seed":202610035096,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":8,\"operation\":\"compare_at_input\",\"u\":9,\"v\":-5,\"x\":3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(8)x+(-2) and g(x)=(9)x+(-5). At the single input x=3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(3)=22 and g(3)=22, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0097","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe5eee1ceffadd647cf875f53eab1743e46365c47880993869c8dde8e76216e0","family_id":"qf-affine-pointwise-comparison","seed":202610035097,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":9,\"operation\":\"compare_at_input\",\"u\":10,\"v\":3,\"x\":-3}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(9)x+(-1) and g(x)=(10)x+(3). At the single input x=-3, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-3)=-28 and g(-3)=-27, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0098","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3454f43ecf2d24dbd496be19ce3c6ed670b9e5944b40854766598224499a3977","family_id":"qf-affine-pointwise-comparison","seed":202610035098,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":10,\"operation\":\"compare_at_input\",\"u\":11,\"v\":2,\"x\":-2}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(10)x+(0) and g(x)=(11)x+(2). At the single input x=-2, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(-2)=-20 and g(-2)=-20, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0099","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf5f99bd247164b2c73749cca5edf19dce7cb14f629ebf4724e812921cdf811a","family_id":"qf-affine-pointwise-comparison","seed":202610035099,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":11,\"operation\":\"compare_at_input\",\"u\":12,\"v\":3,\"x\":-1}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(11)x+(1) and g(x)=(12)x+(3). At the single input x=-1, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"f(-1)=-10 and g(-1)=-9, so the answer is No. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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-r05-linear-function-0100","batch_id":"batch-20261003-r05-linear-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fdc75ee07c468167de00b06a8a2ea074f33c75fe3fbdbc6baef2b04e29545039","family_id":"qf-affine-pointwise-comparison","seed":202610035100,"semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":12,\"operation\":\"compare_at_input\",\"u\":13,\"v\":2,\"x\":0}"},"fields":{"title":"Affine Functions at One Input","stem":"Over R, f(x)=(12)x+(2) and g(x)=(13)x+(2). At the single input x=0, are f(x) and g(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"f(0)=2 and g(0)=2, so the answer is Yes. Equality at this input does not establish equality on the whole domain."},"skills":["Affine Functions at One 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."}}