Question

How to find the asymptotes of `h(x)=5^(x-2)`?

Answer 1

Take the limits of `h(x)` as `x->+-∞` to determine the horizontal asymptotes.

Explanation:

Take the limits of `h(x)` as `x->+-∞` to determine the function's horizontal asymptotes. We have no vertical asymptotes, as there are no values of `x` that will make this function undefined.

`Lim_(x->∞)5^(x-2)=5^∞=∞` (No asymptotes as we approach `+∞`.

`Lim_(x->-∞)5^(x-2)=5^-∞=1/5^∞=0`

So, `y=0` is this function's only horizontal asymptote, as we approach `y=0` for smaller and smaller values of `x` but never cross/touch it.