{"id":"cb_practice_pdf:t7-math-m2-q22","source_id":"cb_practice_pdf","source_item_id":"t7-math-m2-q22","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":2,"position":22,"stem":"x f(x) –4 0 19 – 1 5 18 – 2 5 For the linear function f, the table shows three values of x and their corresponding values of f ( x). If h(x) = f(x)−13, which equation defines h? = 5x−4","stimulus":"","stimulus_html":null,"stem_html":"<p>x f(x) –4 0 19 – 1 5 18 – 2 5 For the linear function f, the table shows three values of x and their corresponding values of f ( x). If h(x) = f(x)−13, which equation defines h? = 5x−4</p>","rationale_html":"<p>Choice B is correct. An equation that defines a linear function f can be written in = + the form f^xh mx b, where m and b are constants. It’s given in the table that =- = - when x 4, f^xh 0. Substituting 4 for x and 0 for f^xh in the equation = + 0= -4 + 0=-4 + f^xh mx b yields m^ h b, or m b. Adding 4m to both sides of = = + this equation yields 4m b. Substituting 4m for b in the equation f^xh mx b 19 = + =- = yields f^xh mx 4m. It’s also given in the table that when x 5, f^xh 1. 19 - = + Substituting 5 for x and 1 for f^xh in the equation f^xh mx 4m yields 1= - 19 +4 1= 1 mb 5 l m, or 5m. Multiplying both sides of this equation by 5 yields = = + =5 +4 5 m 5. Substituting 5 for m in the equation f^xh mx 4m yields f^xh x ^ h, =5 +20 = -13 5 +20 or f^xh x . If h^xh f^xh , substituting x for f^xh in this equation = 5 +20 -13 =5 +7 yields h^xh ^ x h , or h^xh x . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is an equation that defines the linear function f, not h. 44 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2</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>h(x) = 5x+7</p>","ord":0},{"label":"B","content_html":"<p>h(x) = 5x+9</p>","ord":1},{"label":"C","content_html":"<p>h(x) = 5x+20</p>","ord":2},{"label":"D","content_html":"<p>h(x)</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}}