{"id":"cb_question_bank:1dc7239a-dedf-49de-abec-c69f8acd00e6","source_id":"cb_question_bank","source_item_id":"1dc7239a-dedf-49de-abec-c69f8acd00e6","external_id":"a31258b0-0750-420d-9cc1-2b4aad1e6dc2","ibn":null,"question_id":"788bfd56","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 f is defined by f left parenthesis x right parenthesis equals 4 plus StartRoot x EndRoot . What is the value of f left parenthesis 144 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&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 4 plus StartRoot x EndRoot\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mn>4</mn></mrow><mo>+</mo><msqrt><mi>x</mi></msqrt></math>. What is the value of&nbsp;<math alttext=\"f left parenthesis 144 right parenthesis\"><mi>f</mi><mfenced><mrow><mn>144</mn></mrow></mfenced></math>?</p>","rationale_html":"<p>Choice B is correct. The value of&nbsp;<math alttext=\"f left parenthesis 144 right parenthesis\"><mi>f</mi><mfenced><mn>144</mn></mfenced></math> is the value of&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> when <math alttext=\"x equals 144\"><mi>x</mi><mo>=</mo><mn>144</mn></math>.&nbsp;It's given that the function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 4 plus StartRoot x EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></math>. Substituting <math alttext=\"144\"><mn>144</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields&nbsp;<math alttext=\"f left parenthesis 144 right parenthesis equals 4 plus StartRoot 144 EndRoot\"><mi>f</mi><mfenced><mn>144</mn></mfenced><mo>=</mo><mn>4</mn><mo>+</mo><msqrt><mn>144</mn></msqrt></math>. Since the positive square root of <math alttext=\"144\"><mn>144</mn>\n</math> is <math alttext=\"12\"><mn>12</mn>\n</math>, it follows that this equation can be rewritten as <math alttext=\"f left parenthesis 144 right parenthesis equals 4 plus 12\"><mi>f</mi><mfenced><mn>144</mn></mfenced><mo>=</mo><mn>4</mn><mo>+</mo><mn>12</mn></math>, or <math alttext=\"f left parenthesis 144 right parenthesis equals 16\"><mi>f</mi><mfenced><mn>144</mn></mfenced><mo>=</mo><mn>16</mn></math>. Therefore, the value of <math alttext=\"f left parenthesis 144 right parenthesis\"><mi>f</mi><mfenced><mn>144</mn></mfenced></math> is <math alttext=\"16\"><mn>16</mn>\n</math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect. This is the value of&nbsp;<math alttext=\"f left parenthesis 1,296 right parenthesis\"><mi>f</mi><mfenced><mn>1,296</mn></mfenced></math>, not <math alttext=\"f left parenthesis 144 right parenthesis\"><mi>f</mi><mfenced><mn>144</mn></mfenced></math>.</p>\n<p>Choice D is incorrect. This is the value of <math alttext=\"f left parenthesis 5,184 right parenthesis\"><mi>f</mi><mfenced><mn>5,184</mn></mfenced></math>, not&nbsp;<math alttext=\"f left parenthesis 144 right parenthesis\"><mi>f</mi><mfenced><mn>144</mn></mfenced></math>.</p>","correct_answer":["B"],"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=\"0\"><mn>0</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"16\"><mn>16</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"40\"><mn>40</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"76\"><mn>76</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}}