Determine if Odd, Even, or Neither 6x^3-5

$6 x^{3} - 5$

Step 1

Write $6 x^{3} - 5$ as a function.

$f (x) = 6 x^{3} - 5$

Step 2

Find $f (- x)$ .

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

$f (- x) = 6 {(- x)}^{3} - 5$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = 6 ({(- 1)}^{3} x^{3}) - 5$

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

$f (- x) = 6 (- x^{3}) - 5$

Multiply $- 1$ by $6$ .

$f (- x) = - 6 x^{3} - 5$

Step 3

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

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

Since $- 6 x^{3} - 5$ $\neq$ $6 x^{3} - 5$ , the function is not even.

The function is not even

Step 4

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

Find $- f (x)$ .

Multiply $6 x^{3} - 5$ by $- 1$ .

$- f (x) = - (6 x^{3} - 5)$

Apply the distributive property.

$- f (x) = - (6 x^{3}) + 5$

Multiply.

Multiply $6$ by $- 1$ .

$- f (x) = - 6 x^{3} + 5$

Multiply $- 1$ by $- 5$ .

$- f (x) = - 6 x^{3} + 5$

Since $- 6 x^{3} - 5$ $\neq$ $- 6 x^{3} + 5$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6