Determine if Odd, Even, or Neither f(x)=|x|x

$f (x) = | x | x$

Step 1

Reorder factors in $| x | x$ .

$f (x) = x | x |$

Step 2

Find $f (- x)$ .

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = (- x) | - x |$

Make $- x$ positive.

$f (- x) = - x | x |$

Step 3

A function is even if $f (- x) = f (x)$ .

Check if $f (- x) = f (x)$ .

Since $- x | x |$ $\neq$ $x | x |$ , the function is not even.

The function is not even

Step 4

A function is odd if $f (- x) = - f (x)$ .

Remove parentheses.

$- f (x) = - x | x |$

Since $- x | x | = - x | x |$ , the function is odd.

The function is odd

Step 5