{"id":"cb_question_bank:6c56b405-05fc-4cc6-8148-e5fec64cd1cb","source_id":"cb_question_bank","source_item_id":"6c56b405-05fc-4cc6-8148-e5fec64cd1cb","external_id":null,"ibn":"022313-DC","question_id":"271f7e3f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear 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 9, minus, f of 1 ?","stimulus":"f of x equals, the fraction with numerator x plus 7, and denominator 4","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73e457e9eed562fd6f141a031bcac35eafc0b542057152051383f1aa1e602c4d\" alt=\"f of x equals, the fraction with numerator x plus 7, and denominator 4\"></span></span>\n        </p>\n      </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/e7e7e450b69032dac668c8878a6a4e426b7975e3360c1fdcf094a2d953b4738b\" alt=\"f of 9, minus, f of 1\"></span> ?</p>\n","rationale_html":"<p>Choice B is correct. The value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7e7e450b69032dac668c8878a6a4e426b7975e3360c1fdcf094a2d953b4738b\" alt=\"f of 9 minus f of 1 \"></span> can be calculated by finding the values of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c4de9b6ea32181d9b76e121f171026ee0261e56c466ac5e29b06de6d3e61e276\" alt=\"f of 9 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e18f2dd72b8bae075ed41c099e7d195037939975d44bad1b46dd6a0371b05b3c\" alt=\"f of 1\"></span>. The value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c4de9b6ea32181d9b76e121f171026ee0261e56c466ac5e29b06de6d3e61e276\" alt=\"f of 9 \"></span> can be found by substituting 9 for <span class=\"italic\">x</span> in the given function: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d5aca204b6713a71ec211cb23863b7fba7cf45cc64e9371418587e98ae48bb62\" alt=\"f of 9 equals, the fraction with numerator, open parenthesis, 9 plus 7, close parenthesis, and denominator 4\"></span>. This equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e042d230cbfc505c4c184ed1101e73520eaf38b72cdcc8ce4e901892e55b3412\" alt=\"f  of 9 equals, 16 over 4\"></span>, or 4. Then, the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e18f2dd72b8bae075ed41c099e7d195037939975d44bad1b46dd6a0371b05b3c\" alt=\"f of 1\"></span> can be found by substituting 1 for <span class=\"italic\">x </span>in the given function: <span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6244e367b55e09072b6f7ae0fab934fef6ad3787b92ced305b3401944f2a171b\" alt=\"f of 1 equals, the fraction with numerator, open parenthesis, 1 plus 7, close parenthesis, and denominator 4\"></span></span>. This equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/81435f34732d8dff063b0d4bc5aa6ff0610739d7d160475dd8e82d4d6022ceb8\" alt=\"f of 1 equals, 8 over 4\"></span>, or 2. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/75278af2211ee925cd35b7f0553f1b2dddc48737d7f06d4fc24fc61125d81a2d\" alt=\"f of 9 minus f of 1, equals, 4 minus 2\"></span>, which is equivalent to 2.</p><p>Choices A, C, and D are incorrect and may result from incorrectly substituting values of <span class=\"italic\">x</span> in the given function or making computational errors.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f1494c799ca1decbcb94ac7e70aeb91da2c02dfba7cb54dae8e89aee537a8e1\" alt=\"1\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d870b3a6c89096490c39cc291dea5fd94193a953487d36d45d7f8548ac0b8f4e\" alt=\"2\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2cdda43637be35379a891f9cbba6a665ae6aa43f563929757acf84127e4bcef\" alt=\"one fourth\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e9ac80b72304c8d4cbe6587b0262b514ee99e1ffc41a40ecd0e9f38180440de1\" alt=\"nine fourths\"></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}}