{"id":"cb_question_bank:ad77f75d-ffab-4ef4-a3e3-ebc20e09d38b","source_id":"cb_question_bank","source_item_id":"ad77f75d-ffab-4ef4-a3e3-ebc20e09d38b","external_id":"cecc8739-2d4c-4044-8624-baee7ca16ce6","ibn":null,"question_id":"3ea87153","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function g is defined by g left parenthesis x right parenthesis equals x squared plus 9 . For which value of x is g left parenthesis x right parenthesis equals 25 ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function <math alttext=\"g\"><mi>g</mi>\n</math> is defined by <math alttext=\"g left parenthesis x right parenthesis equals x squared plus 9\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>9</mn></mrow></math>. For which value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"g left parenthesis x right parenthesis equals 25\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>25</mn></mrow></math>?</p>","rationale_html":"<p>Choice A is correct. It's given that <math alttext=\"g left parenthesis x right parenthesis equals x squared plus 9\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn></math>. Substituting <math alttext=\"25\"><mn>25</mn>\n</math> for <math alttext=\"g left parenthesis x right parenthesis\"><mi>g</mi><mfenced><mi>x</mi></mfenced></math> in this equation yields <math alttext=\"25 equals x squared plus 9\"><mn>25</mn><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn></math>. Subtracting <math alttext=\"9\"><mn>9</mn>\n</math> from both sides of this equation yields <math alttext=\"16 equals x squared\"><mn>16</mn><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math>. Taking the square root of each side of this equation yields <math alttext=\"x equals plus or minus 4\"><mi>x</mi><mo>=</mo><mo>±</mo><mn>4</mn></math>. It follows that <math alttext=\"g left parenthesis x right parenthesis equals 25\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>25</mn></math> when the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"4\"><mn>4</mn>\n</math> or <math alttext=\"negative 4\"><mo>-</mo><mn>4</mn>\n</math>. Only <math alttext=\"4\"><mn>4</mn>\n</math> is listed among the choices.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.829000+00:00","source_updated_at":"2023-08-02T20:25:59.829000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"4\"><mn>4</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"9\"><mn>9</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"13\"><mn>13</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}