{"id":"cb_question_bank:65d0655b-5d4f-48de-b581-fa2fc909bc13","source_id":"cb_question_bank","source_item_id":"65d0655b-5d4f-48de-b581-fa2fc909bc13","external_id":null,"ibn":"05723-DC","question_id":"5377d9cf","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If f of x equals, the fraction with numerator x squared minus 6 x plus 3, and denominator x minus 1, end fraction , what is f of negative 1 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03e03be526fd873d555d9d8a8f2788e48816db75cb31a9eb9cdd201d1ebbee58\" alt=\"f of x equals, the fraction with numerator x squared minus 6 x plus 3, and denominator x minus 1, end fraction\"></span></span>, what is <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8f25f24d46a87e9f6eedb76babdf083d7cb14da60db1f592188ab520e2d4a213\" alt=\"f of negative 1 \"></span></span> ?</p>\n","rationale_html":"<p>Choice A is correct. Substituting –1 for <span class=\"italic\">x</span> in the equation that defines <span class=\"italic\">f</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/329df3b42a9e972ceec12c7ea129bfe7de2c6aeab232a1f4b779974b31ef9dc1\" alt=\"f of negative 1 equals, the fraction with numerator, open parenthesis, negative 1, close parenthesis, squared, minus 6, times, open parenthesis, negative 1, close parenthesis, plus 3, and denominator negative 1 minus 1, end fraction\"></span>. Simplifying the expressions in the numerator and denominator yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ade95ff1beb5c5b4238622f808d3fd0f40727115eebf1da616b968046a5fcbe2\" alt=\"the fraction with numerator 1 plus 6, plus 3, and denominator negative 2\"></span>, which is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ed6ae282dbdc019b068c2cb538bc05d9ed202bab819daeeaba1e89056410e74e\" alt=\"10 over negative 2\"></span> or –5.</p><p>Choices B, C, and D are incorrect and may result from misapplying the order of operations when substituting –1 for <span class=\"italic\">x</span>. </p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[{"label":"A","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \">–5</span> </span></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \">–2</span> </span></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \">2</span> </span></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \">5</span> </span></p>\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}}