Answer
odd
Work Step by Step
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.
