Determine if Odd, Even, or Neither y=-6x^6-5x^2-2

$y = - 6 x^{6} - 5 x^{2} - 2$

Step 1

Write $y = - 6 x^{6} - 5 x^{2} - 2$ as a function.

$f (x) = - 6 x^{6} - 5 x^{2} - 2$

Step 2

Find $f (- x)$ .

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

$f (- x) = - 6 {(- x)}^{6} - 5 {(- x)}^{2} - 2$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = - 6 ({(- 1)}^{6} x^{6}) - 5 {(- x)}^{2} - 2$

Raise $- 1$ to the power of $6$ .

$f (- x) = - 6 (1 x^{6}) - 5 {(- x)}^{2} - 2$

Multiply $x^{6}$ by $1$ .

$f (- x) = - 6 x^{6} - 5 {(- x)}^{2} - 2$

Apply the product rule to $- x$ .

$f (- x) = - 6 x^{6} - 5 ({(- 1)}^{2} x^{2}) - 2$

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

$f (- x) = - 6 x^{6} - 5 (1 x^{2}) - 2$

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

$f (- x) = - 6 x^{6} - 5 x^{2} - 2$

Step 3

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

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

Since $- 6 x^{6} - 5 x^{2} - 2 = - 6 x^{6} - 5 x^{2} - 2$ , the function is even.

The function is even

Step 4