Determine if Odd, Even, or Neither |x|+x^2+0.001

$| x | + x^{2} + 0.001$

Step 1

Write $| x | + x^{2} + 0.001$ as a function.

$f (x) = | x | + x^{2} + 0.001$

Step 2

Find $f (- x)$ .

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

$f (- x) = | - x | + {(- x)}^{2} + 0.001$

Simplify each term.

Make $- x$ positive.

$f (- x) = | x | + {(- x)}^{2} + 0.001$

Apply the product rule to $- x$ .

$f (- x) = | x | + {(- 1)}^{2} x^{2} + 0.001$

Raise $- 1$ to the power of $2$ .

$f (- x) = | x | + 1 x^{2} + 0.001$

Multiply $x^{2}$ by $1$ .

$f (- x) = | x | + x^{2} + 0.001$

Step 3

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

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

Since $| x | + x^{2} + 0.001 = | x | + x^{2} + 0.001$ , the function is even.

The function is even

Step 4