asymptote

Asymptote

Given a rational function $f(x)=\frac{p(x)}{q(x)}=\frac{a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0}{b_m{x}^m+b_{m-1}{x}^{m-1}+\dots +b_{1}x+b_0}$, then …
If $q(a)=0$ and $p(a)\ne 0$, then $x=a$ is a vertical asymptote.
If $n<m$, then $y=0$ is a horizontal asymptote.
If $n=m$, then $y=\frac{a_n}{b_m}$ is a horizontal asymptote.
If $n>m$, then there are no horizontal asymptotes.