{"id":"cb_practice_pdf:t5-math-m1-q24","source_id":"cb_practice_pdf","source_item_id":"t5-math-m1-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-5","module_number":1,"position":24,"stem":"Which of the following functions has(have) a −3 minimum value at? = −6 3^x −3 I. f x = −3 6^x II. g x","stimulus":"","stimulus_html":null,"stem_html":"<p>Which of the following functions has(have) a −3 minimum value at? = −6 3^x −3 I. f x = −3 6^x II. g x</p>","rationale_html":"<p>= x+ 1 2 Choice D is correct. A function of the form f^xh a^bh c, where a 0 and b 1, is a decreasing function. Both of the given functions are of this form; therefore, both are decreasing functions. If a function f is decreasing, as the value of x increases, the corresponding value of f^xh decreases; therefore, the function doesn’t have a minimum value. Thus, neither of the given functions has a minimum value. 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>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</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}}