Refresher - Even Functions

Refresher

Even functions

${\displaystyle ƒ\left(x\right)=x^2}$ is an example of an even function.

Let ${\displaystyle f\left(x\right)}$be a real-valued function of a real variable. Then f is even if the following equation holds for all x in the domain of ${\displaystyle f}$:

${\displaystyle ƒ\left(x\right)=ƒ(-x)}$

Geometrically, the graph of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis.
Examples of even functions are ${\displaystyle \left|x\right|,x2,x4,cos\left(x\right)}$, and ${\displaystyle cosh\left(x\right)}$.