Question

Let f(x) = tan(x) and g(x) = x − 2.

a. Find and graph f (g(x)). Explain how this graph differs from the graph of tan(x).

b. Find and graph g (f(x)). Explain how this graph differs from the graph of tan(x)

Answer 1

Part A

f(x) = tan(x)

f(g(x)) = tan( g(x) )

f(g(x)) = tan(x-2)

In short, the x has been replaced with x-2. This shifts the entire curve 2 spots to the right. See figure 1 below.

===========================================================

Part B

g(x) = x - 2

g(f(x)) = f(x) - 2

g(f(x)) = tan(x) - 2

The curve shifts down 2 units because we're basically computing y-2 for each y coordinate from f(x) = tan(x). Recall that y = f(x). See figure 2.