{"id":"cb_question_bank:7bbf43d9-8717-47cf-ae08-2e806e855603","source_id":"cb_question_bank","source_item_id":"7bbf43d9-8717-47cf-ae08-2e806e855603","external_id":"3412b211-d5f8-400a-988e-f1dd95e0d2e3","ibn":null,"question_id":"20722644","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 9 . 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 9\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mrow><mn>9</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>Choice C is correct. It's given that <math alttext=\"f left parenthesis x right parenthesis equals x cubed plus 9\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn></math>. Substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields <math alttext=\"f left parenthesis 2 right parenthesis equals left parenthesis 2 right parenthesis cubed plus 9\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><msup><mfenced><mn>2</mn></mfenced><mn>3</mn></msup><mo>+</mo><mn>9</mn></math>. This is equivalent to <math alttext=\"f left parenthesis 2 right parenthesis equals 8 plus 9\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>8</mn><mo>+</mo><mn>9</mn></math>, or&nbsp;<math alttext=\"f left parenthesis 2 right parenthesis equals 17\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>17</mn></math>.</p>\n<p>Choice A is incorrect. This is the value of <math alttext=\"2 plus 3 plus 9\"><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>9</mn></math>, not <math alttext=\"2 cubed plus 9\"><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><mn>9</mn></math>.</p>\n<p>Choice B is incorrect. This is the value of <math alttext=\"2 left parenthesis 3 right parenthesis plus 9\"><mn>2</mn><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>9</mn></math>, not <math alttext=\"2 cubed plus 9\"><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><mn>9</mn></math>.</p>\n<p>Choice D is incorrect. This is the value of <math alttext=\"3 squared plus 9\"><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><mn>9</mn></math>, not <math alttext=\"2 cubed plus 9\"><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><mn>9</mn></math>.</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=\"14\"><mn>14</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"15\"><mn>15</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"17\"><mn>17</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"18\"><mn>18</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}}