Question

What is the asymptote of the function below?

Answer 1

Do you have any guesses as to how the function's graph looks?

Answer 2

A little

Answer 3

So the thing is that it's an exponential function. It grows enormously fast when x gets big. The reverse happens when x gets small (negative). One way to see this is to write it like this:
\[5^{x+3}=\frac{5^3}{5^{-x}}\]
So when x is very "big" and negative, the denominator gets huge, and when you divide by something huge you get something really small. So it approaches zero when x becomes very negative. So y=0 is the asymptote, which is easiest to see if you draw it on paper.