Question

How do you find the horizontal asymptote for `g(x)=5^x`?

Answer 1

`y=0`

Explanation:

For any function f(x), horizontal asymptotes occur at `lim_(x->+-oo)f(x)`.

In this case, `lim_(x->-oo)5^x=0 and lim_(x->oo)5^x=oo`.

hence there is a horizontal asymptote at `y=0`.

This is clear from the graph of the function given below :

graph{5^x [-16.79, 11.69, -4.84, 9.4]}