# How many horizontal asymptotes can the graph of y=f(x) have?

You have to check the end behavior at $\pm \infty$, because they don't have to match.
If the growth rate of the numerator is faster than that of the denominator, you won't have a horizontal asymptote. For example, $f \left(x\right) = {x}^{2}$, it is implied that the denominator is $1$.
If the growth rate of the denominator is faster than that of the numerator, then the horizontal asymptote is $y = 0$. For example, $f \left(x\right) = \frac{1}{x}$.
If the growth rate of the numerator and denominator differ by a constant, $c$, then the horizontal asymptote is $y = c$. Here is a graphical example with 2 horizontal asymptotes $y = - 1$ and $y = 1$: