{"id":"cb_question_bank:a7a8639b-21f8-4b6f-b5ee-dc93f999a93b","source_id":"cb_question_bank","source_item_id":"a7a8639b-21f8-4b6f-b5ee-dc93f999a93b","external_id":"e647a4e3-60a1-4bf3-8ceb-4b40a8d430f1","ibn":null,"question_id":"a26c29f7","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 7 x cubed . In the xy -plane, the graph of y equals g left parenthesis x right parenthesis is the result of shifting the graph of y equals f left parenthesis x right parenthesis down 2 units. Which equation defines function g ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 7 x cubed\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>7</mn></mrow><msup><mi>x</mi><mrow><mn>3</mn></mrow></msup></math>. In the <em>xy</em>-plane, the graph of <math alttext=\"y equals g left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math> is the result of shifting the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> down <math alttext=\"2\"><mn>2</mn>\n</math> units. Which equation defines function <math alttext=\"g\"><mi>g</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. If the graph of <math alttext=\"y equals g left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math> is the result of shifting the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> down <math alttext=\"k\"><mi>k</mi>\n</math> units in the <em>xy</em>-plane, the function <math alttext=\"g\"><mi>g</mi>\n</math> can be defined by an equation of the form <math alttext=\"g left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus k\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mi>k</mi></math>. It’s given that&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 7 x cubed\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup></math> and the graph of&nbsp;<math alttext=\"y equals g left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math> is the result of shifting the graph of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> down <math alttext=\"2\"><mn>2</mn>\n</math> units. Substituting&nbsp;<math alttext=\"7 x cubed\"><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup></math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> and <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"k\"><mi>k</mi>\n</math> in the equation&nbsp;<math alttext=\"g left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus k\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mi>k</mi></math> yields&nbsp;<math alttext=\"g left parenthesis x right parenthesis equals 7 x cubed minus 2\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn></math>.&nbsp;</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This equation defines a function <math alttext=\"g\"><mi>g</mi>\n</math> for which the graph of&nbsp;<math alttext=\"y equals g left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math> is the result of shifting the graph of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> up, not down, <math alttext=\"2\"><mn>2</mn>\n</math> units.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.827000+00:00","source_updated_at":"2023-08-02T20:25:59.827000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"g left parenthesis x right parenthesis equals seven halves x cubed\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mfrac><mn>7</mn><mn>2</mn></mfrac></mrow><msup><mi>x</mi><mrow><mn>3</mn></mrow></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"g left parenthesis x right parenthesis equals 7 x Superscript three halves\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>7</mn></mrow><msup><mi>x</mi><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"g left parenthesis x right parenthesis equals 7 x cubed plus 2\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>7</mn></mrow><msup><mi>x</mi><mrow><mn>3</mn></mrow></msup><mo>+</mo><mrow><mn>2</mn></mrow></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"g left parenthesis x right parenthesis equals 7 x cubed minus 2\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>7</mn></mrow><msup><mi>x</mi><mrow><mn>3</mn></mrow></msup><mo>-</mo><mrow><mn>2</mn></mrow></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}}