Determine if Odd, Even, or Neither -2x^2-9

$- 2 x^{2} - 9$

Step 1

Write $- 2 x^{2} - 9$ as a function.

$f (x) = - 2 x^{2} - 9$

Step 2

Find $f (- x)$ .

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

$f (- x) = - 2 {(- x)}^{2} - 9$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = - 2 ({(- 1)}^{2} x^{2}) - 9$

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

$f (- x) = - 2 (1 x^{2}) - 9$

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

$f (- x) = - 2 x^{2} - 9$

Step 3

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

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

$- 2 x^{2} - 9 = - 2 x^{2} - 9$

Since $- 2 x^{2} - 9 = - 2 x^{2} - 9$ , the function is even.

The function is even

Step 4