Let y = f(x) be a function with domain D = [−6, −2] and range R = [−10, −4]. Find the domain D and range R for each function. Enter your answers using interval notation.

Question

a) y = 1/2f(x)
b) y = f(x-2)+5

Answer 1

(a) clearly, the range is 1/2 the original range, and the domain is unchanged
(b) shift the domain down by 2, and the range up by 5
But, since f(x) is undefined for x outside the interval [-6,-2], the domain must be truncated.