Question

How do you find the asymptote of an exponential function?

Answer 1

There is no vertical asymptote, as `x` may have any value.

Explanation:

For the horizontal asymptote we look at what happens if we let `x` grow, both positively and negatively.

`x->+oo`
The function will be greater without limit. No asymptote there.

`x->-oo`
The function will get smaller and smaller, not ever quite reaching `0`, so `y=0` is an asymptote, or in 'the language':

`lim_(x->-oo) f(x)=0`
graph{0.1*e^x [-30.37, 20.96, -12.52, 13.15]}