# How do you determine if f(x) =root3x is an even or odd function?

Apr 3, 2016

Compare $f \left(- x\right)$ to $f \left(x\right)$.

#### Explanation:

$f \left(- x\right) = \sqrt[3]{- x}$

$= - \sqrt[3]{x}$

$= - f \left(x\right)$

Since $f \left(- x\right) = - f \left(x\right)$, $f \left(x\right)$ is an odd function .


Here is a graph of $y = f \left(x\right)$.
graph{root(3)(x) [-10, 10, -5, 5]}
In addition, if $f \left(x\right)$ is an odd function, if you rotate the graph of $y = f \left(x\right)$ about the origin by 180 degrees, you will get back the same graph. The graph has rotational symmetry about the origin.