Rational function

The rational function $y={\frac {x^{2}-3x-2}{x^{2}-4}}$. 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. $f(x)={\frac {x}{x-3}}$ is a rational function.

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