Function parity

Definition

• A function $f$ is said to be even if $\forall x,fx=f(-x)$, i.e. that is symmetric along the $y$-axis.

• A function $f$ is called odd if $\forall x,fx=-f(-x)$, i.e. that it symmetric rotated 180° around the origin.

The name comes from power functions: the function $fx=x^n$ is even when $n$ is even, and odd when $n$ is odd.