Question

How do you find the domain and range for `(2/3)^x – 9`?

Answer 1

`f(x) = (2/3)^x - 9`

`f(x)` is well defined for all `x in RR` so the domain is `RR`

By looking at end behaviour we find the range of `f(x)` is `(-9, oo)`

Explanation:

As `x->-oo` we have `(2/3)^x = (3/2)^(-x) -> oo`,

so `f(x) -> oo`

As `x->oo` we have `(2/3)^x->0`, so `f(x) -> -9`

So range `f(x) = (-9, oo)`

graph{(2/3)^x - 9 [-22.5, 22.5, -11.25, 11.25]}