{"id":"cb_question_bank:c06be872-82d9-4be1-b1fc-5f6e44ef6dad","source_id":"cb_question_bank","source_item_id":"c06be872-82d9-4be1-b1fc-5f6e44ef6dad","external_id":null,"ibn":"017018-DC","question_id":"dba7432e","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The table above gives the values of the function f for some values of x . Which of the following equations could define f ?","stimulus":"x f ( x ) 0 5 1 five halves 2 five fourths 3 five eighths","stimulus_html":"<div class=\"stimulus_reference\">\n        <table class=\"table_WithBorder tcp-11178d0a-bbd6-4727-92cd-17135268ac70\"><tbody><tr><td class=\"tcp-ca4d8494-78ff-4300-b848-3703b09287f9\">\n                <span class=\"italic\">\n                  <span class=\"italic\">x</span>\n                </span>\n              </td>\n              <td class=\"tcp-5b53cc14-8401-45b5-9507-66a4249218bd\">\n                <span class=\"italic\">\n                  <span class=\"italic\">f</span>\n                </span>(<span class=\"italic\"><span class=\"italic\">x</span></span>)</td>\n            </tr><tr><td class=\"tcp-521d4d07-28b8-4daa-b77d-e0434944d475\">0</td>\n              <td class=\"tcp-5dc6d263-bc4f-4730-b2e3-ca19d275c816\">5</td>\n            </tr><tr><td class=\"tcp-84c9dcf9-429a-4726-94c0-4107ab20e051\">1</td>\n              <td class=\"tcp-88de162c-2093-4e1a-a8b1-65cd689a2425\">\n                <span class=\"math_expression \">\n                  <span class=\"math_expression \">\n                    <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c07dd1b3634a62972e13523df568fe0411662f40a588412490b6b3c77df4e541\" alt=\"five halves\"></span></span>\n                </span>\n              </td>\n            </tr><tr><td class=\"tcp-ee7c5afd-a559-4f13-a01c-ccfd49057622\">2</td>\n              <td class=\"tcp-fa424496-8a6e-4daf-a749-150da6a81bbf\">\n                <span class=\"math_expression \">\n                  <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c551a234fb9895fba855b24b69e02371b2afa96eefaaa668c98e9265c7f35e59\" alt=\"five fourths\"></span></span>\n              </td>\n            </tr><tr><td class=\"tcp-ee7c1cf2-e55b-4101-855b-2ca4d512bb13\">3</td>\n              <td class=\"tcp-77a8bb6e-6139-439b-afa5-e838babaac76\">\n                <span class=\"math_expression \">\n                  <span class=\"math_expression \">\n                    <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c6eeb240719f34197d16d40269302f5b19fac6e06a9c154e225c7aab0177a5eb\" alt=\"five eighths\"></span></span>\n                </span>\n              </td>\n            </tr></tbody></table></div>\n","stem_html":"<p class=\"stem_paragraph \">The table above gives the values of the function <span class=\"italic\">f</span> for some values of <span class=\"italic\">x</span>. Which of the following equations could define <span class=\"italic\">f</span> ?</p>\n","rationale_html":"<p>Choice D is correct. Each choice has a function with coefficient 5 and base 2, so the exponents must be analyzed. When the input value of <span class=\"italic\">x</span> increases, the output value of <span class=\"italic\">f</span>(<span class=\"italic\">x</span>) decreases, so the exponent must be negative. An exponent of –<span class=\"italic\">x</span> yields the values in the table: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c313b7f1fb782522c31235caac1cec36dfbe91a669f2f6a0f52e5a30e95e0dfc\" alt=\"first value, 5, which equals 5 times open parenthesis, 2 to the negative 0 power, close parenthesis\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/644be6d0cd99af2b226cc4e16cbba05ae59af1f3d8bfe3374a18a45c9924a6b8\" alt=\"second value, five halves, which equals 5 times open parenthesis, 2 to the negative 1 power, close parenthesis\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2fedf1f20df9b5b2310235accb5a64362359eb79eff74e9e570e2abb4a9b8472\" alt=\"third value, five fourths, which equals 2 to the negative 2 power\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8132f61168ae8fe01628e23eac575946e2cb9b18743abb83d9f5e6496048033b\" alt=\"fourth value, five eighths, which equals 5 times open parenthesis, 2 to the negative 3 power, close parenthesis\"></span>.</p><p>Choices A and B are incorrect and may result from choosing equations that yield an increasing, rather than decreasing, output value of <span class=\"italic\">f</span>(<span class=\"italic\">x</span>) when the input value of <span class=\"italic\">x</span> increases. Choice C is incorrect and may result from choosing an equation that doesn’t yield the values in the table.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+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/056f1e7dc0e6d10ce8a30b75b3eb456c7061bf9188191b62c696ff3439e32a02\" alt=\"f of x equals, 5 times, open parenthesis, 2 raised to the x plus 1 power, close parenthesis\"></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/64e084431e58f819976cb20edd78f0711522e1ed15a1bf2d439e9d2d188aff49\" alt=\"f of x equals, 5 times, open parenthesis, 2 to the x power, close parenthesis\"></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/e56ed371809d8a865ecf35c5b8ae792ceffad4bf20c5825b287065e6f8d0be3a\" alt=\"f of x equals, 5 times, open parenthesis, 2 raised to the negative, open parenthesis, x plus 1, close parenthesis, power, close parenthesis\"></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/33334a4628bbd6ad21c25ba1b663ac5237c99db7ef1042c123503c06b3c6c1a8\" alt=\"f of x equals, 5 times, open parenthesis, 2 to the negative x power, close parenthesis\"></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}}