Rational function

A rational function is a polynomial divided by a polynomial. ${\displaystyle f(x)={\frac {x}{x-3}}}$ is a rational function.^[1]

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

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

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

References

1. "Rational Functions". dl.uncw.edu. Retrieved March 8, 2018.