{"id":"cb_question_bank:3a59e263-1cc3-4047-9a79-c372ee3a52de","source_id":"cb_question_bank","source_item_id":"3a59e263-1cc3-4047-9a79-c372ee3a52de","external_id":"3c84e10c-eecd-4a7b-b28c-a5de3d455977","ibn":null,"question_id":"837e9da7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":1,"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 StartFraction 1 Over 6 x EndFraction . What is the value of f left parenthesis x right parenthesis when x equals 3 ?","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 StartFraction 1 Over 6 x EndFraction\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mn>6</mn><mi>x</mi></mrow></mfrac></math>. What 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 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that <math alttext=\"f left parenthesis x right parenthesis equals StartFraction 1 Over 6 x EndFraction\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mn>6</mn><mi>x</mi></mrow></mfrac></math>. Substituting <math alttext=\"3\"><mn>3</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields&nbsp;<math alttext=\"f left parenthesis 3 right parenthesis equals StartFraction 1 Over 6 left parenthesis 3 right parenthesis EndFraction\"><mi>f</mi><mfenced><mn>3</mn></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mn>6</mn><mfenced><mn>3</mn></mfenced></mrow></mfrac></math>, or&nbsp;<math alttext=\"f left parenthesis 3 right parenthesis equals one eighteenth\"><mi>f</mi><mfenced><mn>3</mn></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>18</mn></mfrac></math>. Therefore, when <math alttext=\"x equals 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>, the value of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is&nbsp;<math alttext=\"one eighteenth\"><mfrac><mn>1</mn><mn>18</mn></mfrac></math>.</p>\n<p>Choice A is incorrect. This 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 0.5\"><mi>x</mi><mo>=</mo><mn>0.5</mn></math>.</p>\n<p>Choice B is incorrect. This 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 1\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>1</mn>\n</mrow>\n</math>.&nbsp;</p>\n<p>Choice C is incorrect. This 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 1.5\"><mi>x</mi><mo>=</mo><mn>1.5</mn></math>.</p>","correct_answer":["D"],"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=\"one third\"><mfrac>\n\t<mn>1</mn>\n\t<mn>3</mn>\n</mfrac>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"one sixth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>6</mn>\n</mfrac>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"one ninth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>9</mn>\n</mfrac>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"one eighteenth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>18</mn>\n</mfrac>\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}}