{"id":"cb_practice_pdf:t8-math-m1-q26","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q26","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-8","module_number":1,"position":26,"stem":"The functions f and g are defined by the given x ≥ 0 equations, where. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x ≥ 0? f ( x) = 18 ( 1.25)^x +41 I. g x = 9 0.73 II. () ()^x","stimulus":"","stimulus_html":null,"stem_html":"<p>The functions f and g are defined by the given x ≥ 0 equations, where. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x ≥ 0? f ( x) = 18 ( 1.25)^x +41 I. g x = 9 0.73 II. () ()^x</p>","rationale_html":"<p>1.25 Choice B is correct. For the function f, since the base of the exponent, , is 1.25 x greater than 1, the value of ^ h increases as x increases. Therefore, the value 18 1.25 x 18 1.25 x+41 of ^ h and the value of ^ h also increase as x increases. Since f $ is therefore an increasing function where x 0, the function f has no maximum 0.73 value. For the function g, since the base of the exponent, , is less than 1, the 0.73 9 0.73 x x value of ^ h decreases as x increases. Therefore, the value of ^ h also $ decreases as x increases. It follows that the maximum value of g^xh for x 0 = 0 =9 0.73 0 occurs when x 0. Substituting 0 for x in the function g yields g^ h ^ h , 0 =9 1 0 =9 which is equivalent to g^ h ^ h, or g^ h . Therefore, the maximum value of $ g^xh for x 0 is 9, which appears as a coefficient in equation II. So, of the two equations given, only II displays, as a constant or coefficient, the maximum value $ of the function it defines, where x 0. 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 and may result from conceptual or calculation errors.</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>I only</p>","ord":0},{"label":"B","content_html":"<p>II only</p>","ord":1},{"label":"C","content_html":"<p>I and II</p>","ord":2},{"label":"D","content_html":"<p>Neither I nor II STO</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}}