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

$f (x) = x + | x |$

Step 1

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 2

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 3

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

Find $- f (x)$ .

Multiply $x + | x |$ by $- 1$ .

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

Apply the distributive property.

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

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

The function is not odd

Step 4

The function is neither odd nor even

Step 5