{"id":"cb_practice_pdf:t6-math-m2-q24","source_id":"cb_practice_pdf","source_item_id":"t6-math-m2-q24","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-6","module_number":2,"position":24,"stem":"t__ The function f is defined by f(x) = a x+b, where a and b are constants. In the xy-plane, the graph of = f(x) (−24,0) y passes through the point, and f(24) < 0. Which of the following must be true? f(0) = 24","stimulus":"","stimulus_html":null,"stem_html":"<p>t__ The function f is defined by f(x) = a x+b, where a and b are constants. In the xy-plane, the graph of = f(x) (−24,0) y passes through the point, and f(24) &lt; 0. Which of the following must be true? f(0) = 24</p>","rationale_html":"<p>24 10 24 Choice D is correct. It’s given that f^ h . Substituting for f^xh in the = + 24 = 24+ 24+ 10 equation f^xh a x b yields f^ h a b. Therefore, a b . Since 24+ 1 b can’t be negative, it follows that a 0. It’s also given that the graph of = -24,0 =-24 = y f^xh passes through the point ^ h. It follows that when x , f^xh 0. -24 = + Substituting for x and 0 for f^xh in the equation f^xh a x b yields 0= -24+ = -24+ =0 a b. By the zero product property, either a 0 or b . 1 24+ =0 Since a 0, it follows that b . Squaring both sides of this equation yields -24+ =0 24 =24 b . Adding to both sides of this equation yields b . Since 1 24 1 a 0 and b is , it follows that a b must be true. Choice A is incorrect. The value of f^0h is a b, which must be negative. Choice B -24 is incorrect. The value of f^0h is a b, which could be , but doesn’t have to be. Choice C is incorrect and may result from conceptual or calculation errors. 50 SAT PRACTICE TEST #6 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>f(0) = −24</p>","ord":0},{"label":"B","content_html":"<p>&gt;</p>","ord":1},{"label":"C","content_html":"<p>a b &lt;</p>","ord":2},{"label":"D","content_html":"<p>a b</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}}