Determine if Odd, Even, or Neither |x-3|

$| x - 3 |$

Step 1

Write $| x - 3 |$ as a function.

$f (x) = | x - 3 |$

Step 2

Find $f (- x)$ .

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

$f (- x) = | (- x) - 3 |$

Remove parentheses.

$f (- x) = | - x - 3 |$

Step 3

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

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

$| - x - 3 |$ $\neq$ $| x - 3 |$

Since $| - x - 3 |$ $\neq$ $| x - 3 |$ , the function is not even.

The function is not even

Step 4

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

Multiply $- 1$ by $| x - 3 |$ .

$- f (x) = - | x - 3 |$

Since $| - x - 3 |$ $\neq$ $- | x - 3 |$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6