For each of the functions below, state the domain and range, the restrictions, the intervals of increasing and decreasing, the roots, y-intercepts, and vertices.

Question

a)
f(x)=2x(^2)−8

b)
f(x)=+√x-2

Answer 1

domain of all exponentials is (-∞,∞)
Range of a^x is (0,∞), so I'm sure you can adjust that as needed here.

you know that the domain of √x is [0,∞), so now you just have to adjust to make sure that x-2 >= 0.
As for the range, just recall that square roots are never negative.