$f(x)$ is an odd function.
Work Step by Step
To check if the function is odd, we must check whether it complies to the rule for an odd function $-f(x) = f(-x)$. In order to do this, we'll plug in a random x-value into our function to see whether it works for the rule. Let's use the x-value $1$. Does $-f(1) = f(-1)$? Plug in function in place of f. $-[(1)*|1|] ?=? [(-1)*|-1|]$ $-(1*1) ?=? (-1)*(1)$ $-1 = -1$ Seeing that our function complies with the rule for an odd function, we can conclude that our function $f(x)$ is odd.