{"id":"cb_question_bank:acc07060-1405-4054-bfe2-db4d47f4ab2f","source_id":"cb_question_bank","source_item_id":"acc07060-1405-4054-bfe2-db4d47f4ab2f","external_id":"35058beb-41fe-4d27-9257-454cd92cb3f3","ibn":null,"question_id":"3c600337","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"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 270 left parenthesis 0.1 right parenthesis Superscript x . What is the value of f left parenthesis 0 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 270 left parenthesis 0.1 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>270</mn></mrow><msup><mfenced><mn>0.1</mn></mfenced><mi>x</mi></msup></math>. What is the value of&nbsp;<math alttext=\"f left parenthesis 0 right parenthesis\"><mi>f</mi><mfenced><mn>0</mn></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. The value of <math alttext=\"f left parenthesis 0 right parenthesis\"><mi>f</mi><mfenced><mn>0</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 0\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given function yields <math alttext=\"f left parenthesis 0 right parenthesis equals 270 left parenthesis 0.1 right parenthesis Superscript 0\"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>270</mn><msup><mfenced><mn>0.1</mn></mfenced><mn>0</mn></msup></math>, or <math alttext=\"f left parenthesis 0 right parenthesis equals 270 left parenthesis 1 right parenthesis\"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>270</mn><mfenced><mn>1</mn></mfenced></math>, which is equivalent to <math alttext=\"f left parenthesis 0 right parenthesis equals 270\"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>270</mn></math>. Therefore, the value of <math alttext=\"f left parenthesis 0 right parenthesis\"><mi>f</mi><mfenced><mn>0</mn></mfenced></math> is <math alttext=\"270\"><mn>270</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math>, not <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the value of <math alttext=\"f left parenthesis 1 right parenthesis\"><mi>f</mi><mfenced><mn>1</mn></mfenced></math>, not <math alttext=\"f left parenthesis 0 right parenthesis\"><mi>f</mi><mfenced><mn>0</mn></mfenced></math>.</p>","correct_answer":["D"],"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=\"0\"><mn>0</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"1\"><mn>1</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"27\"><mn>27</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"270\"><mn>270</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}}