{"id":"cb_question_bank:59ed643d-fa6a-4d6e-bf76-4c833699a0a0","source_id":"cb_question_bank","source_item_id":"59ed643d-fa6a-4d6e-bf76-4c833699a0a0","external_id":"91bb6f2f-9d21-4a10-add7-5e0ad39aece8","ibn":null,"question_id":"6ecdbcb4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals left parenthesis x plus 6 right parenthesis left parenthesis x plus 5 right parenthesis left parenthesis x minus 4 right parenthesis The function f is given. Which table of values represents y equals f left parenthesis x right parenthesis minus 3 ?","stimulus":"","stimulus_html":null,"stem_html":"

f(x)=(x+6)(x+5)(x-4)

\n

The function f\n is given. Which table of values represents y=f(x)-3?

","rationale_html":"

Choice B is correct. It’s given that fx=(x+6)(x+5)(x-4) and y=f(x)-3. Substituting (x+6)(x+5)(x-4) for fx in the equation y=f(x)-3 yields y=(x+6)(x+5)(x-4)-3. Substituting -6\n for x\n in this equation yields y=(-6+6)(-6+5)(-6-4)-3, or \n\ty\n\t=\n\t-3\n\n. Substituting -5\n for x\n in the equation y=(x+6)(x+5)(x-4)-3 yields y=(-5+6)(-5+5)(-5-4)-3, or \n\ty\n\t=\n\t-3\n\n. Substituting 4\n for x\n in the equation y=(x+6)(x+5)(x-4)-3 yields y=(4+6)(4+5)(4-4)-3, or \n\ty\n\t=\n\t-3\n\n. Therefore, when \n\tx\n\t=\n\t-6\n\n then \n\ty\n\t=\n\t-3\n\n, when \n\tx\n\t=\n\t-5\n\n then \n\ty\n\t=\n\t-3\n\n, and when \n\tx\n\t=\n\t4\n\n then \n\ty\n\t=\n\t-3\n\n. Thus, the table of values in choice B represents y=f(x)-3.

\n

Choice A is incorrect. This table represents \n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n rather than y=f(x)-3.

\n

Choice C is incorrect. This table represents \n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t3\n\t\n\n rather than y=f(x)-3.

\n

Choice D is incorrect. This table represents y=fx+3 rather than y=f(x)-3.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":true,"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":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-9\n
-5\n-8\n
4\n1\n
","ord":0},{"label":"B","content_html":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-3\n
-5\n-3\n
4\n-3\n
","ord":1},{"label":"C","content_html":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-3\n
-5\n-2\n
4\n7\n
","ord":2},{"label":"D","content_html":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n3\n
-5\n3\n
4\n3\n
","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}}