Rational function

The rational function [math]\displaystyle{ y=\frac{x^2-3x-2}{x^2-4} }[/math]. The dotted lines are the asymptotes.

The curve gets closer and closer to touching the asymptote (the red line) but never does.

A rational function is a polynomial divided by a polynomial. [math]\displaystyle{ f(x)=\frac{x}{x-3} }[/math] is a rational function.

An asymptote is a line that a curve gets closer and closer to touching but never does.