Rational functions/Real numbers/Introduction/Section

Next to the polynomial functions, the simplest functions are the rational functions.

A fraction ${}P/Q$ of polynomials may be considered as a function which is defined outside the zeroes of the denominator. The example shows the graph of the rationale function ${}1/X$.

Definition

For polynomials ${}P,Q\in \mathbb {R} [X]$, ${}Q\neq 0$, the function

$D\longrightarrow \mathbb {R} ,z\longmapsto {\frac {P(z)}{Q(z)}},$

where ${}D$ is the complement of the zeroes

of ${}Q$, is called a rational function.