{"id":"cb_practice_pdf:t7-math-m1-q16","source_id":"cb_practice_pdf","source_item_id":"t7-math-m1-q16","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-7","module_number":1,"position":16,"stem":"= x−4x_I The function f is defined by f(x). What 1 f(5)−f(a) = −15 value of a satisfies? −20","stimulus":"","stimulus_html":null,"stem_html":"<p>= x−4x_I The function f is defined by f(x). What 1 f(5)−f(a) = −15 value of a satisfies? −20</p>","rationale_html":"<p>= - Choice C is correct. It’s given that the function f is defined by f^xh x 4x . It’s 5 - =-15 also given that f^ h f^ah . Substituting 5 for x in the function = - 5 = 5-4 5 f^xh x 4x yields f^ h ^ h and substituting a for x in the function = - = - 5 =15 = - f^xh x 4x yields f^ah a 4a . Therefore, f^ h and f^ah 3a . 15 - 5 - =-15 Substituting for f^5h and 3a for f^ah in the equation f^ h f^ah 15- -3 =-15 15 yields a . Subtracting from both sides of this equation yields - -3 =-30 - -3 =30 a . Dividing both sides of this equation by 1 yields a . By -3 =30 -3 =30 -3 =-30 the definition of absolute value, if a , then a or a . - =-10 =10 Dividing both sides of each of these equations by 3 yields a or a , respectively. Thus, of the given choices, a value of a that satisfies 5 - =-15 10 f^ h f^ah is . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"","ord":0},{"label":"B","content_html":"<p>5</p>","ord":1},{"label":"C","content_html":"<p>10</p>","ord":2},{"label":"D","content_html":"<p>45</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}