{"id":"cb_question_bank:7920c1a6-6025-4af5-aac7-917faf03dbed","source_id":"cb_question_bank","source_item_id":"7920c1a6-6025-4af5-aac7-917faf03dbed","external_id":null,"ibn":"05013-DC","question_id":"c651cc56","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Some values of the linear function f are shown in the table above. What is the value of f of 3 ?","stimulus":"The figure presents a 2-column table, with 3 rows of data. The heading for the first column is “x,” and the heading for the second column is “f of x.” The 3 rows of data are as follows. Row 1. x, zero; f of x, negative 2. Row 2. x, 2; f of x, 4. Row 3. x, 6; f of x, 16.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <div class=\"image-options-wrapper image-wrap-center 47704 tcp-3c67b4f5-9949-4c4c-a080-a2acef10554c\">\n            <img src=\"/api/assets/145144cc20115591b213b391926e33228df09f2fd9d5fc74e21b236696f78962\" alt=\"The figure presents a 2-column table, with 3 rows of data. The heading for the first column is “x,” and the heading for the second column is “f of x.” The 3 rows of data are as follows. \nRow 1. x, zero; f of x, negative 2. \nRow 2. x, 2; f of x, 4.\nRow 3. x, 6; f of x, 16.\n\" width=\"78\" height=\"73\"></div>\n        </div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Some values of the linear function <span class=\"italic\">f </span>are shown in the table above. What is the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2941316e5e47bc3a1dc8048bc5063aaa540fd944bb9266acea6b11614dabf6ef\" alt=\"f of 3\"></span>?</p>\n","rationale_html":"<p>Choice B is correct. A linear function has a constant rate of change, and any two rows of the table shown can be used to calculate this rate. From the first row to the second, the value of <span class=\"italic\">x</span> is increased by 2 and the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26d9f477bb154c8ef7637e64827776ac5831aa760a31d21a53157367bd210b16\" alt=\"f of x\"></span> is increased by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26a480e5c522590fa078b36475267d0e70e30e09880019ffeb0abb57bb7eb56f\" alt=\"6 equals, 4 minus negative 2\"></span>. So the values of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26d9f477bb154c8ef7637e64827776ac5831aa760a31d21a53157367bd210b16\" alt=\"f of x\"></span> increase by 3 for every increase by 1 in the value of <span class=\"italic\">x</span>. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9baa2f23dcc4298d9cf63300be81f00c46fbe353aa8d308d3f74381ffe4a2897\" alt=\"f of 2, equals 4\"></span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3fce1a57dc532804ad65d5b2d45b2d67a52828bab10590a31c2f7097d3f25a22\" alt=\"f of, open parenthesis, 2 plus 1, close parenthesis, equals, 4 plus 3, which equals 7\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/882e0436d2b58aba397bb60234eb9d264188ae74869db09cb4bbcce398043eb6\" alt=\"f of 3, equals 7\"></span>.</p><p>Choice A is incorrect. This is the third <span class=\"italic\">x</span>-value in the table, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2941316e5e47bc3a1dc8048bc5063aaa540fd944bb9266acea6b11614dabf6ef\" alt=\"f of 3\"></span>. Choices C and D are incorrect and may result from errors when calculating the function’s rate of change.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[{"label":"A","content_html":"<p>6</p>\n","ord":0},{"label":"B","content_html":"<p>7</p>\n","ord":1},{"label":"C","content_html":"<p>8</p>\n","ord":2},{"label":"D","content_html":"<p>9</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}}