Question

How do you find the intercepts, asymptotes and graph `f(x)=5^x-2`?

Answer 1

This function is simply `5^x` shifted downwards of `2` units. So, the only asymptote is `y=-2` (since the original one was `y=0`) as `x\to-\infty`.

As for the intercepts: the `y` intercept is found by setting `x=0`, and you have `5^0-2 = 1-2=-1`.
The `x` intercept is found by setting `f(x)=y=0`, and you have

`5^x-2=0 \iff 5^x=2 \iff x=log_5(2)`.

As I already said, the graph of this function is simply the graph of `5^x` shifted downwards of `2` units.