{"id":"cb_question_bank:fad52911-8e5b-4d8f-9f63-6cfbf9bf6687","source_id":"cb_question_bank","source_item_id":"fad52911-8e5b-4d8f-9f63-6cfbf9bf6687","external_id":null,"ibn":"04172-DC","question_id":"1a722d7d","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Let the function p be defined as p of x equals, the fraction with numerator, open parenthesis, x minus c, close parenthesis, squared, plus, 160, and denominator, 2 c , end fraction , where c is a constant. If p of c equals, 10 , what is the value of p of 12 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Let the function&nbsp;<span class=\"italic\">p</span> be defined as <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a37276180164c4269bf8d76a3f3f69efa8f321303d77c9b9ac8e23f58d3ff97d\" alt=\"p of x equals, the fraction with numerator, open parenthesis, x minus c, close parenthesis, squared, plus, 160, and denominator, 2 c , end fraction\"></span></span>, where&nbsp;<span class=\"italic\">c</span> is a constant. <span class=\"formatted_line_break delivery_mode:PPT \"></span>If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d64ec002437eb250e021d1721eec00279eb3ad8308d763fd1fe4e71cc52b9a4\" alt=\"p of c equals, 10\"></span></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/6fd23ea5b3adf6b48f2e8b722b7547c83abe8154f886fa431f64d296c13fa75c\" alt=\"p of 12\"></span></span> ?</p>\n","rationale_html":"<p>Choice D is correct. The value of <span class=\"italic\">p</span>(12) depends on the value of the constant <span class=\"italic\">c</span>, so the value of <span class=\"italic\">c</span> must first be determined. It is given that <span class=\"italic\">p</span>(<span class=\"italic\">c</span>) = 10. Based on the definition of <span class=\"italic\">p</span>, it follows that:</p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/791b4f06bf088004c1c117ab2a9f0ae3ff760573d1dbf2b69afc7e12b1cc7bdb\" alt=\"p of c equals, the fraction with numerator open parenthesis, c minus c, close parenthesis, squared, plus 160, and denominator 2 c, end fraction, which equals 10\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1deb6ca06e1babacdbb6b53f06cf9c1b665c3c03d37ed7ca9cdbbd9a54857765\" alt=\"the fraction 160 over 2 c, end fraction, equals 10\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f9b7aaabad95755d9d5a4c56ed7441763c32ec12c2738fc82d358ae0082b8bc\" alt=\"2 c equals 16\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e53439ffa5a36b7748e2065bc2c494ea25642662d2f9aa59254484a550416e54\" alt=\"c equals 8\"></span></p><p>This means that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13dedb01229620168e7fa564254cd4a032be23b9f00bdbcd1898c6f077736655\" alt=\"p of x equals, the fraction with numerator open parenthesis, x minus 8, close parenthesis, squared, plus 160, and denominator 16\"></span> for all values of <span class=\"italic\">x</span>. Therefore:</p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/66d91f0978831c3bbd6ec2eea9ec34564e77ab30461568542fac496a22b9c496\" alt=\"p of 12 equals, the fraction with numerator open parenthesis, 12 minus 8, close parenthesis, squared, plus 160, and denominator 16\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/960fe7ae29c65fd2d15c5a47f10c0e8c2c79aedd3da03fc2765683afcc968a5c\" alt=\"which equals the fraction with numerator 16 plus 160, and denominator 16\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/08db2aeb2755688d1e89edad072fabd2ab56fe2fbf8c15eb6f0d42a9906e52eb\" alt=\"which equals 11\"></span></p><p>Choice A is incorrect. It is the value of <span class=\"italic\">p</span>(8), not <span class=\"italic\">p</span>(12). Choices B and C are incorrect. If one of these values were correct, then<span class=\"italic\"> x</span> = 12 and the selected value of <span class=\"italic\">p</span>(12) could be substituted into the equation to solve for <span class=\"italic\">c</span>. However, the values of <span class=\"italic\">c</span> that result from choices B and C each result in <span class=\"italic\">p</span>(<span class=\"italic\">c</span>) &lt; 10.</p><p></p>\n","correct_answer":["D"],"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>10.00</p>\n","ord":0},{"label":"B","content_html":"<p>10.25</p>\n","ord":1},{"label":"C","content_html":"<p>10.75</p>\n","ord":2},{"label":"D","content_html":"<p>11.00</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}}