Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x).     x           −2            −1            0            1            2          f(x)           −2            −1            −3            1            2          x           −1            0            1            2            3          g(x)           −2            −1            −3            1            2          x           −2            −1            0            1            2          h(x)           3            4            2            6            7      g(x)= h(x)=

Write the function g(x) in terms of the function f(r). Og(x) = -3f(x) +2 Og(2) = -f(2) – 2 O g(x) = f(x) +2 Og(z) = -f(x) – 3

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)} =

The transformation of a function f(x)f(x) into a function g(x)g(x) is given by g(x) = Af(Bx + H) + K g(x) — Af(Ba + н) + К. where the constants • AA vertically scales the function. (negative A reflects the function about the x-axis.) • BB 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) = - 2 · f(x + 2) - 2 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.) 4 -б -5 -4 -3 -2 -7 6 -1 -2 -3 -4 -5 |-6+