Determine if Odd, Even, or Neither (|x|)/2-3

$\frac{| x |}{2} - 3$

Step 1

Write $\frac{| x |}{2} - 3$ as a function.

$f (x) = \frac{| x |}{2} - 3$

Step 2

Find $f (- x)$ .

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

$f (- x) = \frac{| - x |}{2} - 3$

Make $- x$ positive.

$f (- x) = \frac{| x |}{2} - 3$

Step 3

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

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

Since $\frac{| x |}{2} - 3 = \frac{| x |}{2} - 3$ , the function is even.

The function is even

Step 4