The function f is defined by f x = a 2.2 x + 2.2 b , where a and b

Question

The function f is defined by f x = a 2.2 x + 2.2 b , where a and b are integer constants and 0 &#60; a &#60; b . 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 y -intercept of the graph of y = f x in the xy -plane as a constant or coefficient? g x = a 2.2 x + k h x = a 2.2 x + m

Accepted Answer

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 equation defining function f yields f 0 = a 2.2 0 + 2.2 b , or f 0 = a 1 + 2.2 b . So, the y -coordinate of the y -intercept of the graph is a 1 + 2.2 b , or equivalently, a + a 2.2 b . It's given that function g is equivalent to function f , where 0 < a < b . It follows that k = 2.2 b . Since a 2.2 b can't be equal to 0 , the coefficient a can't be equal to a + a 2.2 b . Since 0 < a , the constant k , which is equal to 2.2 b , can't be equal to a + a 2.2 b . Therefore, function g doesn't display the y -coordinate of the y -intercept of the graph of y = f x 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 defining f can be rewritten as f x = a 2.2 x + a 2.2 b . It follows that m = a 2.2 b . Since a 2.2 b can't be equal to 0 , the coefficient a can't be equal to a + a 2.2 b . Since 0 < a , the constant m , which is equal to a 2.2 b , can't be equal to a + a 2.2 b . Therefore, function h doesn't display the y -coordinate of the y -intercept of the graph of y = f x 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 x 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.

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