{"id":"cb_question_bank:a00dab5d-7964-4501-b3ad-7f18e94ab4fc","source_id":"cb_question_bank","source_item_id":"a00dab5d-7964-4501-b3ad-7f18e94ab4fc","external_id":"a6fb9475-3880-4ae5-952c-4bbb83ee59af","ibn":null,"question_id":"09f58996","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":3,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f left parenthesis x right parenthesis equals 6 plus StartRoot x EndRoot . What is the value of f left parenthesis 36 right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 6 plus StartRoot x EndRoot\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mn>6</mn></mrow><mo>+</mo><msqrt><mi>x</mi></msqrt></math>. What is the value of <math alttext=\"f left parenthesis 36 right parenthesis\"><mi>f</mi><mfenced><mrow><mn>36</mn></mrow></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"12\"><mn>12</mn>\n</math>. The value of <math alttext=\"f left parenthesis 36 right parenthesis\"><mi>f</mi><mfenced><mn>36</mn></mfenced></math> is the value of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> when <math alttext=\"x equals 36\"><mi>x</mi><mo>=</mo><mn>36</mn></math>. Substituting <math alttext=\"36\"><mn>36</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation yields <math alttext=\"f left parenthesis 36 right parenthesis equals 6 plus StartRoot 36 EndRoot\"><mi>f</mi><mfenced><mn>36</mn></mfenced><mo>=</mo><mn>6</mn><mo>+</mo><msqrt><mn>36</mn></msqrt></math>, which is equivalent to&nbsp;<math alttext=\"f left parenthesis 36 right parenthesis equals 6 plus 6\"><mi>f</mi><mfenced><mn>36</mn></mfenced><mo>=</mo><mn>6</mn><mo>+</mo><mn>6</mn></math>, or <math alttext=\"f left parenthesis 36 right parenthesis equals 12\"><mi>f</mi><mfenced><mn>36</mn></mfenced><mo>=</mo><mn>12</mn></math>. Thus, the value of <math alttext=\"f left parenthesis 36 right parenthesis\"><mi>f</mi><mfenced><mn>36</mn></mfenced></math> is <math alttext=\"12\"><mn>12</mn>\n</math>.</p>","correct_answer":["12"],"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":[],"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}}