## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\text{odd}$
Recall: a) A function is said to be odd, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=-f(x)$ b) A function is said to be even, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=f(x)$ Replace $x$ with $-x$ to evaluate $f(-x)$: $f(-x)=\dfrac{2(-x)}{|-x|} \\=-\dfrac{2x}{|x|} \\=-f(x)$ Therefore, the function $f(x)$ is odd.