Determine if Odd, Even, or Neither -8x^3

$- 8 x^{3}$

Step 1

Write $- 8 x^{3}$ as a function.

$f (x) = - 8 x^{3}$

Step 2

Find $f (- x)$ .

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

$f (- x) = - 8 {(- x)}^{3}$

Apply the product rule to $- x$ .

$f (- x) = - 8 ({(- 1)}^{3} x^{3})$

Raise $- 1$ to the power of $3$ .

$f (- x) = - 8 (- x^{3})$

Multiply $- 1$ by $- 8$ .

$f (- x) = 8 x^{3}$

Step 3

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

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

$8 x^{3}$ $\neq$ $- 8 x^{3}$

Since $8 x^{3}$ $\neq$ $- 8 x^{3}$ , the function is not even.

The function is not even

Step 4

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

Multiply $- 8$ by $- 1$ .

$- f (x) = 8 x^{3}$

Since $8 x^{3} = 8 x^{3}$ , the function is odd.

The function is odd

Step 5