Precalculus Examples

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

Step 1

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

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

Step 2

Find $f (- x)$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Dividing two negative values results in a positive value.

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

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

The function is even

Step 4