Precalculus Examples

$f (x) = 4 x^{3}$

Step 1

Find $f (- x)$ .

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Step 1.1

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

$f (- x) = 4 {(- x)}^{3}$

Step 1.2

Apply the product rule to $- x$ .

$f (- x) = 4 ({(- 1)}^{3} x^{3})$

Step 1.3

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

$f (- x) = 4 (- x^{3})$

Step 1.4

Multiply $- 1$ by $4$ .

$f (- x) = - 4 x^{3}$

Step 2

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

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Step 2.1

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

Step 2.2

Since $- 4 x^{3}$ $\neq$ $4 x^{3}$ , the function is not even.

The function is not even

Step 3

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

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Step 3.1

Multiply $4$ by $- 1$ .

$- f (x) = - 4 x^{3}$

Step 3.2

Since $- 4 x^{3} = - 4 x^{3}$ , the function is odd.

The function is odd

Step 4