Precalculus Examples

$f (x) = \frac{x^{3}}{7 x^{2}}$

Step 1

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $x^{3}$ .

$f (x) = \frac{x^{2} x}{7 x^{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x^{2}$ out of $7 x^{2}$ .

$f (x) = \frac{x^{2} x}{x^{2} \cdot 7}$

Step 1.2.2

Cancel the common factor.

$f (x) = \frac{x^{2} x}{x^{2} \cdot 7}$

Step 1.2.3

Rewrite the expression.

$f (x) = \frac{x}{7}$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = \frac{- x}{7}$

Step 2.2

Move the negative in front of the fraction.

$f (- x) = - \frac{x}{7}$

Step 3

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

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Step 3.1

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

Step 3.2

Since $- \frac{x}{7}$ $\neq$ $\frac{x}{7}$ , the function is not even.

The function is not even

Step 4

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

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Step 4.1

Multiply $- 1$ by $\frac{x}{7}$ .

$- f (x) = - \frac{x}{7}$

Step 4.2

Since $- \frac{x}{7} = - \frac{x}{7}$ , the function is odd.

The function is odd

Step 5