## Precalculus (10th Edition)

We know that if a function is odd, then $f(-x)=-f(x).$ We know that if a function is even, then $f(-x)=f(x).$ Hence, we plug in $-x$ into $x$ and see what happens. \begin{align*} f(-x)&=\frac{2(-x)}{|-x|}\\ &=\frac{-2x}{|x|}\\ &=-f(x) \end{align*} Therefore the function is odd.