{"id":"cb_question_bank:d571f807-2a80-40fa-9dc1-1dc62f6523c7","source_id":"cb_question_bank","source_item_id":"d571f807-2a80-40fa-9dc1-1dc62f6523c7","external_id":"b0bf4cfd-4fbe-4424-acc0-d7a7f44468f7","ibn":null,"question_id":"79ba511a","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 x cubed plus 15 . What is the value of f left parenthesis 2 right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals x cubed plus 15\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mrow><mn>15</mn></mrow></math>. What is the value of <math alttext=\"f left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mrow><mn>2</mn></mrow></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. The value of <math alttext=\"f left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mn>2</mn></mfenced></math> is the value of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>&nbsp;when <math alttext=\"x equals 2\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>2</mn>\n</mrow>\n</math>. Substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given function yields <math alttext=\"f left parenthesis 2 right parenthesis equals left parenthesis 2 right parenthesis cubed plus 15\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><msup><mfenced><mn>2</mn></mfenced><mn>3</mn></msup><mo>+</mo><mn>15</mn></math>, or&nbsp;<math alttext=\"f left parenthesis 2 right parenthesis equals 8 plus 15\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>8</mn><mo>+</mo><mn>15</mn></math>, which is equivalent to <math alttext=\"f left parenthesis 2 right parenthesis equals 23\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>23</mn></math>. Therefore, the value of <math alttext=\"f left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mn>2</mn></mfenced></math> is <math alttext=\"23\"><mn>23</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the value of <math alttext=\"f left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mn>2</mn></mfenced></math>&nbsp;when <math alttext=\"f left parenthesis x right parenthesis equals x left parenthesis 3 right parenthesis plus 15\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>15</mn></math>, rather than <math alttext=\"f left parenthesis x right parenthesis equals x cubed plus 15\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>15</mn></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"20\"><mn>20</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"21\"><mn>21</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"23\"><mn>23</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"24\"><mn>24</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}}