# Periodic Functions

**
Periodic functions
**
are
functions
that behave in a cyclic (repetitive) manner over a specified interval (called a period). The graph repeats itself over and over as it is traced from left to right. In other words, the entire graph can be formed from copies of a particular portion, repeated at regular intervals indefinitely. If
$f$
is known over one period then it is known everywhere.

More formally, a function $f$ is periodic if there exists a real number $P$ such that $f\left(x+P\right)=f\left(x\right)$ for all $x$ .