{"id":"cb_practice_pdf:t9-math-m1-q22","source_id":"cb_practice_pdf","source_item_id":"t9-math-m1-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-9","module_number":1,"position":22,"stem":"Function f is defined by f(x) = (x+6)(x+5)(x+1). Function g is defined = f(x−1) y = g(x) by g(x). The graph of in the (a,0) (b,0) (c,0) xy-plane has x-intercepts at,, and, where a, b, and c are distinct constants. What is the a+b+c value of? −15","stimulus":"","stimulus_html":null,"stem_html":"<p>Function f is defined by f(x) = (x+6)(x+5)(x+1). Function g is defined = f(x−1) y = g(x) by g(x). The graph of in the (a,0) (b,0) (c,0) xy-plane has x-intercepts at,, and, where a, b, and c are distinct constants. What is the a+b+c value of? −15</p>","rationale_html":"<p>= - = +6 +5 +1 Choice B is correct. It’s given that g^xh f^x 1h. Since f^xh ^x h^x h^x h, -1 = -1+6 -1+5 -1+1 it follows that f^x h ^x h^x h^x h. Combining like terms -1 = +5 +4 = +5 +4 yields f^x h ^x h^x h^xh. Therefore, g^xh x^x h^x h. The = x-intercepts of a graph in the xy-plane are the points where y 0. The = x-coordinates of the x-intercepts of the graph of y g^xh in the xy-plane can be 0= +5 +4 found by solving the equation x^x h^x h. Applying the zero product = +5=0 +4=0 property to this equation yields three equations: x 0, x , and x . = =- =- Solving each of these equations for x yields x 0, x 5, and x 4, = 0,0 respectively. Therefore, the x-intercepts of the graph of y g^xh are ^ h, -5,0 -4,0 - - ^ h, and ^ h. It follows that the values of a, b, and c are 0, 5, and 4. + + 0+ -5 + -4 - Thus, the value of a b c is ^ h ^ h, which is equal to 9. + + = + Choice A is incorrect. This is the value of a b c if g^xh f^x 1h. Choice C is + + - = -6 -51 - incorrect. This is the value of a b c 1 if g^xh ^x h^xx h^ h. Choice D + + = -6 -5 -1 is incorrect. This is the value of a b c if f^xh ^x h^x h^x h.</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":"","ord":0},{"label":"B","content_html":"<p>−9 11</p>","ord":1},{"label":"C","content_html":"<p>15</p>","ord":2},{"label":"D","content_html":"","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}}