{"id":"cb_question_bank:740a6886-7296-4cdf-8ca5-d250bc3569c8","source_id":"cb_question_bank","source_item_id":"740a6886-7296-4cdf-8ca5-d250bc3569c8","external_id":null,"ibn":"032723-DC","question_id":"75915e3c","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":2,"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 2 ?","stimulus":"f of x equals, 2 times, open parenthesis, 3 raised to the x power, close parenthesis","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/bf129866b326b7d62dbfc2bdb2a2ba67d167e4f857cb3fe912dd0660ae13f2f7\" alt=\"f of x equals, 2 times, open parenthesis, 3 raised to the x power, close parenthesis\"></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/c534a5a7cf84ff0c1cd81dff96930fca311cecf67f58b25ebb4ae7baceba1574\" alt=\"f of 2\"></span>?</p>\n","rationale_html":"<p>Choice C is correct. The value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c534a5a7cf84ff0c1cd81dff96930fca311cecf67f58b25ebb4ae7baceba1574\" alt=\"f of 2 \"></span> is found by evaluating the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/438d1b301e07b2c4d77bfa1542d37a3bc9972ce1792bdeff915f02637fcc8472\" alt=\"2 times 3 raised to the x power\"></span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span>. 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/af78c1cb2ec24f0cc34483b2241c0bcd55b544164b232d1b372ebe33b23e82af\" alt=\"f of 2 equals, 2 times, 3 squared\"></span>. Simplifying <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ce1458c4cbd0b65d529f41ced4b9b42337ac6c05acaec75d283c202c8bea2d9\" alt=\"3 squared \"></span> in the equation results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/22bbb39d493dcdd8548bbac4bd520e8977e120f04279a907599b6480e5a49716\" alt=\"f of 2 equals, 2 times 9\"></span>. Evaluating the right-hand side of the equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d6a189c992c6155519807e0f2af8194bf191e8cb3b97dee1b211d5f1ece69611\" alt=\"f of 2 equals 18\"></span>. Therefore, the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c534a5a7cf84ff0c1cd81dff96930fca311cecf67f58b25ebb4ae7baceba1574\" alt=\"f of 2 \"></span> is 18.</p><p>Choice A is incorrect and may result from evaluating the expression as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f87501a5aec439a0ebf5f950cccbc654e0f4a02eec661196915d311044507c43\" alt=\"3 squared\"></span>. Choice B is incorrect and may result from evaluating the expression as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0caf2c715a33aa232c7934c56441e3eb2a4c91a58ae2a3681c2cbb27c9e99dc3\" alt=\"2 times, open parenthesis, 3 times 2, close parenthesis\"></span>. Choice D is incorrect and may result from evaluating the expression as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9b736692a9f30a81eba1a33cd685b463c5878b5584b747ee924c737f5911ff3a\" alt=\"open parenthesis, 2 times 3, close parenthesis, squared\"></span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">9</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">12</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">18</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">36</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}}