Rational function

• A function $f$ is called a rational function if it can be written in the form $f(x)=\frac{P(x)}{Q(x)}$ where $P$ and $Q$ are polynomial functions of $x$ and $Q$ is not the zero function.
  • $\text{dom}(f)=\{x\mid Q(x)\ne 0\}$
  • A rational function is proper if $\mathrm{deg}P<\mathrm{deg}Q$, otherwise it is improper.