{"id":"cb_question_bank:f75d3af4-8a7c-4f55-a972-23183cc14cc2","source_id":"cb_question_bank","source_item_id":"f75d3af4-8a7c-4f55-a972-23183cc14cc2","external_id":"585130f5-a566-4db1-900e-4f8d08cd67e6","ibn":null,"question_id":"981aca65","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 StartFraction a minus 19 Over x EndFraction plus 5 In the given function f , a is a constant. The graph of function f in the xy -plane, where y equals f left parenthesis x right parenthesis , is translated 3 units down and 4 units to the right to produce the graph of y equals g left parenthesis x right parenthesis . Which equation defines function g ?","stimulus":"","stimulus_html":null,"stem_html":"

fx=a-19x+5

\n

In the given function f\n, a\n is a constant. The graph of function f\n in the xy-plane, where y=fx, is translated 3\n units down and 4\n units to the right to produce the graph of y=gx. Which equation defines function g\n?

","rationale_html":"

Choice B is correct. It's given that the graph of y=gx is produced by translating the graph of y=fx 3\n units down and 4\n units to the right in the xy-plane. Therefore, function g\n can be defined by an equation in the form gx=fx-4-3. Function f is defined by the equation fx=a-19x+5, where a\n is a constant. Substituting x-4 for x\n in the equation fx=a-19x+5 yields fx-4=a-19x-4+5. Substituting a-19x-4+5 for fx-4 in the equation gx=fx-4-3 yields gx=a-19x-4+5-3, or gx=a-19x-4+2. Therefore, the equation that defines function g\n is gx=a-19x-4+2.

\n

Choice A is incorrect. This equation defines a function whose graph is produced by translating the graph of y=fx 3\n units down and 4\n units to the left, not 3\n units down and 4\n units to the right.

\n

Choice C is incorrect. This equation defines a function whose graph is produced by translating the graph of  y=fx 4\n units to the left, not 3\n units down and 4\n units to the right.

\n

Choice D is incorrect. This equation defines a function whose graph is produced by translating the graph of y=fx 4\n units to the right, not 3\n units down and 4\n units to the right.

","correct_answer":["B"],"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":"

gx=a-19x+4+2

","ord":0},{"label":"B","content_html":"

gx=a-19x-4+2

","ord":1},{"label":"C","content_html":"

gx=a-22x+4+5

","ord":2},{"label":"D","content_html":"

gx=a-22x-4+5

","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}}