b The function f is defined by f(x) = a ( 2.2^x +2.2), 0 < a < b where a and b are integer constants and. The functions g and h are equivalent to function f, where k and m are constants. Which of the following equations displays the y-coordinate of the = f(x) y-intercept of the graph of y in the xy-plane as a constant or coefficient? g(x) = a(2.2^x +k) I. h ( x) = a (2.2)^x + m II.
","rationale_html":"Choice D is correct. A y-intercept of a graph in the xy-plane is a point where the = graph intersects the y-axis, or a point where x 0. Substituting 0 for x in the 0 = 2.20+2.2 b 0 = 1+2.2 b equation defining function f yields f^ h a^ h, or f^ h a^ h. So, 1+2.2 b the y-coordinate of the y-intercept of the graph is a^ h, or equivalently, + 2.2 b < < a a^ h . It’s given that function g is equivalent to function f, where 0 a b. It =2.2 b 2.2 b follows that k . Since a^ h can’t be equal to 0, the coefficient a can’t be + 2.2 b < 2.2 b equal to a a^ h . Since 0 a, the constant k, which is equal to , can’t be + 2.2 b equal to a a^ h . Therefore, function g doesn’t display the y-coordinate of the = y-intercept of the graph of y f^xh in the xy-plane as a constant or coefficient. It’s < < also given that function h is equivalent to function f, where 0 a b. The equation = 2.2 x+ 2.2 b = 2.2 b defining f can be rewritten as f^xh a^ h a^ h . It follows that m a^ h . 2.2 b + 2.2 b Since a^ h can’t be equal to 0, the coefficient a can’t be equal to a a^ h . < 2.2 b + 2.2 b Since 0 a, the constant m, which is equal to a^ h , can’t be equal to a a^ h . Therefore, function h doesn’t display the y-coordinate of the y-intercept of the = graph of y f^xh in the xy-plane as a constant or coefficient. Thus, neither function g nor function h displays the y-coordinate of the y-intercept of the = graph of y f^xh in the xy-plane as a constant or coefficient. 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.
","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":"I only
","ord":0},{"label":"B","content_html":"II only
","ord":1},{"label":"C","content_html":"I and II
","ord":2},{"label":"D","content_html":"Neither I nor II STO
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