Use the function f plotted below to define g(x) = | f(t)dt y=f(x) -2 2 -2 Answer the following questions about the function g(x). a. Evaluate: g(0) • g(4) • g(-3) 2.

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 9(х) — — 2- f(а+ 3) + 3 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: Transform the function by applying the constants in this order: H, B, A, K.) 6+ 4 -6 -5 -4 -3 -2 -1 2 3 4 5 -2 -3 -4 -5 -6+ Clear All Draw: Dot Line Segment

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. Let f(x) = 2x + 1 and g(x) = a. Determine the domain and range of both f(x) and g(x). b. Find (g o f)(x). c. Determine the domain of (g o f)(x).