{"id":"cb_question_bank:af6bbceb-7fb1-4a21-a7b4-7d19ecdf231c","source_id":"cb_question_bank","source_item_id":"af6bbceb-7fb1-4a21-a7b4-7d19ecdf231c","external_id":"7fedd1ee-8dd3-449f-8f4a-8154d1d099ed","ibn":null,"question_id":"042aa429","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If f ( x ) = x + 7 and g ( x ) = 7 x , what is the value of 4 f ( 2 ) − g ( 2 ) ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">If <math><mrow><mi>f</mi><mrow><mo stretchy=\"true\" fence=\"true\" form=\"prefix\">(</mo><mrow><mi>x</mi></mrow><mo stretchy=\"true\" fence=\"true\" form=\"postfix\">)</mo></mrow><mo>=</mo><mi>x</mi><mo>+</mo><mrow><mn>7</mn></mrow></mrow></math> and <math><mrow><mi>g</mi><mrow><mo stretchy=\"true\" fence=\"true\" form=\"prefix\">(</mo><mrow><mi>x</mi></mrow><mo stretchy=\"true\" fence=\"true\" form=\"postfix\">)</mo></mrow><mo>=</mo><mrow><mn>7</mn></mrow><mi>x</mi></mrow></math>, what is the value of <math><mrow><mrow><mn>4</mn></mrow><mi>f</mi><mrow><mo stretchy=\"true\" fence=\"true\" form=\"prefix\">(</mo><mrow><mrow><mn>2</mn></mrow></mrow><mo stretchy=\"true\" fence=\"true\" form=\"postfix\">)</mo></mrow><mo>−</mo><mi>g</mi><mrow><mo stretchy=\"true\" fence=\"true\" form=\"prefix\">(</mo><mrow><mrow><mn>2</mn></mrow></mrow><mo stretchy=\"true\" fence=\"true\" form=\"postfix\">)</mo></mrow></mrow></math>?</p>","rationale_html":"<p>Choice C is correct. The value of <math alttext=\"f left parenthesis 2 right parenthesis\"><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> can be found by substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation <math alttext=\"f left parenthesis x right parenthesis equals x plus 7\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mn>7</mn></math>, which yields <math alttext=\"f left parenthesis 2 right parenthesis equals 2 plus 7\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>2</mn><mo>+</mo><mn>7</mn></math>, or&nbsp;<math alttext=\"f left parenthesis 2 right parenthesis equals 9\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>9</mn></math>. The value of <math alttext=\"g left parenthesis 2 right parenthesis\"><mi>g</mi><mfenced><mn>2</mn></mfenced></math> can be found by substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation&nbsp;<math alttext=\"g left parenthesis x right parenthesis equals 7 x\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>7</mn><mi>x</mi></math>, which yields&nbsp;<math alttext=\"g left parenthesis 2 right parenthesis equals 7 left parenthesis 2 right parenthesis\"><mi>g</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>7</mn><mfenced><mn>2</mn></mfenced></math>, or&nbsp;<math alttext=\"g left parenthesis 2 right parenthesis equals 14\"><mi>g</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>14</mn></math>. The value of the expression&nbsp;<math alttext=\"4 f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis\"><mn>4</mn><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>-</mo><mi>g</mi><mfenced><mn>2</mn></mfenced></math>&nbsp;can be found by substituting the corresponding values into the expression, which gives <math alttext=\"4 left parenthesis 9 right parenthesis minus 14\"><mn>4</mn><mo>(</mo><mn>9</mn><mo>)</mo><mo>−</mo><mn>14</mn></math>. This expression is equivalent to <math alttext=\"36 minus 14\"><mn>36</mn><mo>-</mo><mn>14</mn></math>, or <math alttext=\"22\"><mn>22</mn>\n</math>.</p>\n<p>Choice A is incorrect. This is the value of <math alttext=\"f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis\"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>-</mo><mi>g</mi><mfenced><mn>2</mn></mfenced></math>, not&nbsp;<math alttext=\"4 f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis\"><mn>4</mn><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>-</mo><mi>g</mi><mfenced><mn>2</mn></mfenced></math>.</p>\n<p>Choice B is incorrect and may result from calculating&nbsp;<math alttext=\"4 f left parenthesis 2 right parenthesis\"><mn>4</mn><mi>f</mi><mfenced><mn>2</mn></mfenced></math> as <math alttext=\"4 left parenthesis 2 right parenthesis plus 7\"><mn>4</mn><mo>(</mo><mn>2</mn><mo>)</mo><mo>+</mo><mn>7</mn></math>, rather than<br><math alttext=\"4 left parenthesis 2 plus 7 right parenthesis\"><mn>4</mn><mo>(</mo><mn>2</mn><mo>+</mo><mn>7</mn><mo>)</mo></math>.</p>\n<p>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":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math><mn>-5</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math><mn>1</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math><mn>22</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math><mn>28</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}}