{"id":"cb_practice_pdf:t11-math-m2-q17","source_id":"cb_practice_pdf","source_item_id":"t11-math-m2-q17","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":17,"stem":"17 x g x ^ h 1 32 2 28 3 24 4 20 For the linear function g, the table shows four values of x and their corresponding values of g x. The ^ h = + function can be written as g x mx b, where m ^ h and b are constants. What is the value of b?","stimulus":"","stimulus_html":null,"stem_html":"<p>17 x g x ^ h 1 32 2 28 3 24 4 20 For the linear function g, the table shows four values of x and their corresponding values of g x. The ^ h = + function can be written as g x mx b, where m ^ h and b are constants. What is the value of b?</p>","rationale_html":"<p>Choice D is correct. It’s given that for the linear function g, the table shows four values of x and their corresponding values of g^xh. It’s also given that the = + function can be written as g^xh mx b, where m and b are constants. The table 32 shows that when the value of x is 1, the corresponding value of g^xh is . 32 = + 32= 1 + Substituting 1 for x and for g^xh in g^xh mx b yields m^ h b, or 32= + 32- = m b. Subtracting b from both sides of this equation yields b m. The table also shows that when the value of x is 2, the corresponding value of g^xh is 28 28 = + 28= 2 + . Substituting 2 for x and for g^xh in g^xh mx b yields m^ h b, or 28=2 + 32- 28=2 32- + m b. Substituting b for m in this equation yields ^ bh b. Applying the distributive property to the right-hand side of this equation yields 28=64-2 + 28=64- 64 b b, or b. Subtracting from both sides of this equation -36=- - 36= yields b. Dividing both sides of this equation by 1 yields b. 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 C is incorrect and may result from conceptual or calculation errors.</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>4</p>","ord":0},{"label":"B","content_html":"<p>16</p>","ord":1},{"label":"C","content_html":"<p>32</p>","ord":2},{"label":"D","content_html":"<p>36</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}}