Precalculus Examples

$y = \frac{\tan (x)}{x}$

Step 1

Write $y = \frac{\tan (x)}{x}$ as a function.

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

Step 2

Find $f (- x)$ .

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

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

Since $\tan (- x)$ is an odd function, rewrite $\tan (- x)$ as $- \tan (x)$ .

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

Dividing two negative values results in a positive value.

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

Step 3

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

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

$\frac{\tan (x)}{x} = \frac{\tan (x)}{x}$

Since $\frac{\tan (x)}{x} = \frac{\tan (x)}{x}$ , the function is even.

The function is even

Step 4