{"id":"cb_question_bank:e8d4a66a-9e69-4d8e-807a-201f6c1548e0","source_id":"cb_question_bank","source_item_id":"e8d4a66a-9e69-4d8e-807a-201f6c1548e0","external_id":"6343862e-4b55-4888-a763-6c005c8707e0","ibn":null,"question_id":"de362c2f","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 5 x squared . What is the value of f left parenthesis 8 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 5 x squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>5</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></math>. What is the value of&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mrow><mn>8</mn></mrow></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. 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 5 x squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup></math>. Substituting <math alttext=\"8\"><mn>8</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in <math alttext=\"f left parenthesis x right parenthesis equals 5 x squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup></math> yields&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis equals 5 left parenthesis 8 right parenthesis squared\"><mi>f</mi><mfenced><mn>8</mn></mfenced><mo>=</mo><mn>5</mn><msup><mfenced><mn>8</mn></mfenced><mn>2</mn></msup></math>, which is equivalent to <math alttext=\"f left parenthesis 8 right parenthesis equals 5 left parenthesis 64 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced><mo>=</mo><mn>5</mn><mfenced><mn>64</mn></mfenced></math>, or&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis equals 320\"><mi>f</mi><mfenced><mn>8</mn></mfenced><mo>=</mo><mn>320</mn></math>. Therefore, the value of&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> is <math alttext=\"320\"><mn>320</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the value of&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> if&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 5 x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>5</mn><mi>x</mi></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the value of&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> if&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 5 left parenthesis x plus 2 right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>5</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the value of&nbsp;<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> if&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals left parenthesis 5 x right parenthesis left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced><mrow><mn>5</mn><mi>x</mi></mrow></mfenced><mfenced><mn>2</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=\"40\"><mn>40</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"50\"><mn>50</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"80\"><mn>80</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"320\"><mn>320</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}}