{"id":"cb_question_bank:d67879bc-b16b-4cf3-88d4-9d7ff51bccfe","source_id":"cb_question_bank","source_item_id":"d67879bc-b16b-4cf3-88d4-9d7ff51bccfe","external_id":null,"ibn":"021098-DC","question_id":"023c0a8d","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For the function f , if f of open parenthesis, 3 x, close parenthesis, equals x minus 6 for all values of x , what is the value of f of 6 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">For the function <span class=\"italic \">f</span>, if <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cefc8c50614d63018f9809b464f7d44089063d339fa761fdd74771c2d937592\" alt=\"f of open parenthesis, 3 x, close parenthesis, equals x minus 6\"></span></span> for all values of <span class=\"italic\">x</span>, what is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bdb5d529d42df488477a31e3021dca1fcd89e757a89dd8b02408e30a1b1deef9\" alt=\"f of 6 \"></span></span> ?</p>\n","rationale_html":"<p>Choice B is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cefc8c50614d63018f9809b464f7d44089063d339fa761fdd74771c2d937592\" alt=\"f of 3 x, equals x minus 6\"></span> for all values of <span class=\"italic\">x</span>. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c160227574ea14449cd2c900271d05b13762e246b0d35aed92df79c31cfd6925\" alt=\"3 x equals 6\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a6e3f5e7a0e7e066cce4e1dfb5893b799a028a971b889bd3be384e3f9147e3b5\" alt=\"f of 3 x\"></span> will equal <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bdb5d529d42df488477a31e3021dca1fcd89e757a89dd8b02408e30a1b1deef9\" alt=\"f of 6\"></span>. Dividing both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c160227574ea14449cd2c900271d05b13762e246b0d35aed92df79c31cfd6925\" alt=\"3 x equals 6 \"></span> by 3 gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span>. Therefore, substituting 2 for <span class=\"italic\">x</span> in the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d866de81c9bc4c03cdc6138f74257c72fb32b49ed384bcdb174cd5cbbd42a88a\" alt=\"f of, open parenthesis, 3 times 2, close parenthesis, equals 2 minus 6\"></span>, which can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0a8c7b518883c936e7f10e80da98034d26ce8af67f6a67135ee76e9defd538db\" alt=\"f of 6, equals negative 4\"></span>.</p><p>Choice A is incorrect. This is the value of the constant in the given equation for <span class=\"italic\">f</span>. Choice C is incorrect and may result from substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b1023e15d50cb679a3c030c38974bb902514afa9f233eff14c3d4466e78ba4d\" alt=\"x equals 6\"></span>, rather than <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span>, into the given equation. Choice D is incorrect. This is the value of <span class=\"italic\">x</span> that yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bdb5d529d42df488477a31e3021dca1fcd89e757a89dd8b02408e30a1b1deef9\" alt=\"f of 6 \"></span> for the left-hand side of the given equation; it’s not the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bdb5d529d42df488477a31e3021dca1fcd89e757a89dd8b02408e30a1b1deef9\" alt=\"f of 6 \"></span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ac4e862b233acbee95c501658ff49dd21661d2a931c76a597fe7d20c5d70df\" alt=\"negative 6\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc0609d3d5523eaf8e35097c2a9c872ba31206db61297d0a21597123b1c843d7\" alt=\"negative 4\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/89503a15bc55359ac0221507f66997a6362731fc08bff905bf4f85df48a32ed3\" alt=\"0\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab0e8b338371b48a8fba8a54e84c5da5fca4f9e4bbe0ae3e4e1d3dfa0c514a36\" alt=\"2\"></span></span>\n          </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}}