Question

What is the equation of the horizontal asymptote of `g(x)=5^x+4`?

Answer 1

The horizontal asymptote is `y=4`

Explanation:

To look for a horizontal asymptote,
we find the limit of `g(x)` as `x->+-oo`

limit `(5^x+4)=5^(+oo)+4=+oo`
`x->+oo`

limit `(5^x+4)=5^(-oo)+4=1/5^(+oo)+4=0+4`
`x->-oo`

So `y=4` is a horizontal asymptote
graph{(y-5^x-4)(y-4)=0 [-11.12, 4.675, 0.12, 8.02]}