Find the Maclaurin polynomial of degree 3 for the function. f(x) = e-x

The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H)+ K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) : = 3· f(x) The function f (x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 구 4 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -2- -3- -4- -5- -6- -7- Clear All Draw: Dot Line Segment Question Help:

2. Determine two non-equivalent polynomials f(x) and g(x), such that f(0) = g(0) and f(1) = g(1).

Express each function as a composition of two functions. (Find f(x) and g(x) such that the given function equals (fog)(x). Assume g(x) ‡ x.) (a) F(x) = √√√7x + 6 {f(x), g(x)} = (b) G(x) = 18x 71 {f(x), g(x)} = (c) H(x) = (ax + b)² {f(x), g(x)} = (d) T(x) = 1/√x {f(x), g(x)} =