{"id":"cb_practice_pdf:t7-math-m1-q17","source_id":"cb_practice_pdf","source_item_id":"t7-math-m1-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":"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":1,"position":17,"stem":"f(0) For the^- exponential function f,^- the value of is c, where c is a constant. Of the following equations that define the function f, which equation shows the value of c as the coefficient or the base? f(x) = 22(1.5)^x+1","stimulus":"","stimulus_html":null,"stem_html":"<p>f(0) For the^- exponential function f,^- the value of is c, where c is a constant. Of the following equations that define the function f, which equation shows the value of c as the coefficient or the base? f(x) = 22(1.5)^x+1</p>","rationale_html":"<p>Choice B is correct. Each of the given choices is an equation of the form = x - k f^xh a^bh , where a, b, and k are constants. For an equation of this form, the coefficient, a, is equal to the value of the function when the exponent is equal to = =33 1.5 x 0, or when x k. It follows that in the equation f^xh ^ h , the coefficient, 33, is equal to the value of f^0h. Substituting 0 for x in this equation yields 0 =33 1.5 0 0 =33 1 0 =33 f^ h ^ h , which is equivalent to f^ h ^ h, or f^ h . Thus, the value of =33 1.5 x c is 33 and the equation f^xh ^ h shows the value of c as the coefficient. - Choice A is incorrect. This equation shows the value of f^ 1h, not f^0h, as the coefficient. Choice C is incorrect. This equation shows the value of f^1h, not f^0h, as the coefficient. Choice D is incorrect. This equation shows the value of f^2h, not f^0h, as the coefficient.</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>( ) = 33(1.5)^x</p>","ord":0},{"label":"B","content_html":"<p>f x f(x) = 49.5(1.5)^x^−1</p>","ord":1},{"label":"C","content_html":"<p>f(x) = 74.25(1.5)^x^−2</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}}