asymptote

An asymptote is a curve that continuously approaches a given curve (function) but does not meet it at any finite distance.

To find an asymptote, consider a function $f(x)$ in the following format: $f(x)=\frac{N(x)}{D(x)}$

To find vertical asymptotes, set $D(x)=0$, and solve for $x$.

To find horizontal asymptotes, find the limit of $f(x)$ as $x$ approaches positive or negative infinitive. In other words:

$$\underset{x\to \pm \infty }{\lim }f(x)$$