Question

If r(x)=2-x^2 and w(x)=x-2, what is the range of (w*r)(x)

Answer 1

First, find the product (w*r)(x): (w*r)(x) = (x-2)*[2-x^2] = 2x - x^3 - 4 + 2x^2

This is a cubing function. Since the sign of the cube-of-x term is negative, the graph will begin in Quadrant II and pass through Quadrant IV. There are no limits on y. Thus, the range is (-infinity, +infinity).