Even/Odd Functions

A function is even if, for each $x$ in the domain of $f$ , $f (- x) = f (x)$ . Even functions have reflective symmetry across the $y$ -axis.

Example of an even function:

$\begin{array}{l} f (x) = x^{2} \\ f (- x) = {(- x)}^{2} = x^{2} = f (x) \end{array}$

A function is odd if, for each $x$ in the domain of $f$ , $f (- x) = - f (x)$ . Odd functions have $180 °$ rotational symmetry about the origin.

Example of an odd function:

$\begin{array}{l} f (x) = x^{3} \\ f (- x) = {(- x)}^{3} = - x^{3} = - f (x) \end{array}$