{"id":"cb_practice_pdf:t11-math-m2-q18","source_id":"cb_practice_pdf","source_item_id":"t11-math-m2-q18","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":null,"form_id":"cb_practice_pdf:test-11","module_number":2,"position":18,"stem":"18 x 24 30 32 f x -8 -8 8 ^ h For the quadratic function f, the table shows three values of x and their corresponding values of f x. ^ h Which equation defines f?","stimulus":"","stimulus_html":null,"stem_html":"<p>18 x 24 30 32 f x -8 -8 8 ^ h For the quadratic function f, the table shows three values of x and their corresponding values of f x. ^ h Which equation defines f?</p>","rationale_html":"<p>24 =-8 30 =-8 32 =8 Choice B is correct. According to the table, f^ h , f^ h , and f^ h . = + Let the quadratic function g be defined by g^xh f^xh 8. Therefore, 24 = 24 +8 30 = 30 +8 32 = 32 +8 - g^ h f^ h , g^ h f^ h , and g^ h f^ h . Substituting 8 for 24 24 = 24 +8 24 =-8+8 24 =0 f^ h in the equation g^ h f^ h yields g^ h , or g^ h . - 30 30 = 30 +8 30 =-8+8 Substituting 8 for f^ h in the equation g^ h f^ h yields g^ h , 30 =0 32 32 = 32 +8 or g^ h . Substituting 8 for f^ h in the equation g^ h f^ h yields 32 =8+8 32 =16 24 =0 30 =0 g^ h , or g^ h . By the factor theorem, if g^ h and g^ h , = -24 -30 32 =16 then g^xh k^x h^x h, where k is a constant. Since g^ h , 32 16 = -24 -30 substituting for x and for g^xh in the equation g^xh k^x h^x h 16= 32-24 32-30 16= 8 2 16=16 yields k^ h^ h, or k^ h^ h, which is equivalent to k. 16 = Dividing both sides of this equation by yields 1 k. Substituting 1 for k in the = -24 -30 = -24 -30 equation g^xh k^x h^x h yields g^xh ^x h^x h. Since = + - = g^xh f^xh 8, it follows that g^xh 8 f^xh. Subtracting 8 from both sides of the = -24 -30 -8= -24 -30 -8 equation g^xh ^x h^x h yields g^xh ^x h^x h . Substituting - = -24 -30 -8 f^xh for g^xh 8 in this equation yields f^xh ^x h^x h . 47 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 =24 Choice A is incorrect. If this equation defined f, then when x , the value of - f^xh would be 4, not 8. Choice C is incorrect. If this equation defined f, then =32 32 when x , the value of f^xh would be , not 8. Choice D is incorrect. If this =32 -32 equation defined f, then when x , the value of f^xh would be , not 8.</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>f x = x - 24 x - 30 + 4 ^ h ^ h^ h = - - -</p>","ord":0},{"label":"B","content_html":"<p>f x x 24 x 30 8 ^ h ^ h^ h = - - +</p>","ord":1},{"label":"C","content_html":"<p>f x x 8 x 32 32 ^ h ^ h^ h</p>","ord":2},{"label":"D","content_html":"<p>f x = x - 8 x - 32 - 32 ^ h ^ h^ h</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}}