{"id":"cb_question_bank:63b1be0c-abe4-4083-874e-db717872b03e","source_id":"cb_question_bank","source_item_id":"63b1be0c-abe4-4083-874e-db717872b03e","external_id":null,"ibn":"029384-DC","question_id":"78d5f91a","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":"For the function f defined above, what is the value of f of negative 1 ?","stimulus":"f of x equals, x cubed, plus 3 x squared, minus 6 x, minus 1","stimulus_html":"<div class=\"stimulus_reference \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b9ce4d522ebfa7ee274bad498b8eb703e10d283328073b5f161b397081b8ec4\" alt=\"f of x equals, x cubed, plus 3 x squared, minus 6 x, minus 1\"></span></span></div>\n","stem_html":"<p class=\"stem_paragraph \">For the function <span class=\"italic\">f</span> defined above, what is the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8f25f24d46a87e9f6eedb76babdf083d7cb14da60db1f592188ab520e2d4a213\" alt=\"f of negative 1\"></span>?</p>\n","rationale_html":"<p>Choice C is correct. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span> for <span class=\"italic\">x</span> in the given function <span class=\"italic\">f</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0a2a3f481b7f7305ca7662c8479b676a5c8fffb9edcee9c0ff121d50810aeff1\" alt=\"f of negative 1 equals, open parenthesis, negative 1, close parenthesis, cubed, plus 3 times, open parenthesis, negative 1, close parenthesis, squared, minus, 6 times negative 1, minus 1\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3bca5ca1674485fc35df68e23d2d738dcf52455ba0e281b3e0ad9e69ec69a27f\" alt=\"f of negative 1 equals, negative 1 plus, 3 times 1, minus, 6 times negative 1, minus 1\"></span>. This further simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92aa75834d7c823fe92e0bbcbd4967f050acb667ab96da83499b5d6174433685\" alt=\"f of negative 1 equals, negative 1 plus 3, plus 6, minus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2cb95d831047be12a506ee3706695905663851507999a650677f4c354ad1b56\" alt=\"f of negative 1, equals 7\"></span>.</p><p>Choice A is incorrect and may result from correctly substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1 \"></span> for <span class=\"italic\">x</span> in the function but incorrectly simplifying the resulting expression to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1d80847e6f1c7b0935acc1ea9ef5f479f0cc8938736991f6768e8cdff883dc55\" alt=\"f of negative 1 equals, negative 1 minus 3, minus 6, minus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/05ceac8a98ce4d369b607796d28ca3edb483023c0c4e20448f1c484da9264337\" alt=\"negative 11\"></span>. Choice B is incorrect and may result from arithmetic errors. Choice D is incorrect and may result from correctly substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span> for <span class=\"italic\">x</span> in the function but incorrectly simplifying the expression to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6a798c27ffdbfd5a49c57737be81f65462c47752abc185999404060e690ee3fd\" alt=\"f of negative 1 equals, 1 plus 3, plus 6, plus 1\"></span>, or 11.</p><p>&nbsp;</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.625000+00:00","source_updated_at":"2023-08-02T20:25:59.625000+00:00","options":[{"label":"A","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/05ceac8a98ce4d369b607796d28ca3edb483023c0c4e20448f1c484da9264337\" alt=\"negative 11\"></span></p><p>&nbsp;</p><p></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1b363b7d8efa0458a458105037fd9ee9a31e28b0361c9535991bcaccd678576\" alt=\"negative 7\"></span></p><p>&nbsp;</p><p></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aa4f2bc9f9d9e942987ab37126748b20a9f78e4ca3c017d7462926f46ed61f09\" alt=\"7\"></span></p><p>&nbsp;</p><p></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c1182628fe39061898436aa0ec45cb84592c1a2248485646c7d23133df30d3c\" alt=\"11\"></span></p><p>&nbsp;</p><p></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}}