Precalculus Examples

$f (x) = x$

Step 1

Find $f (- x)$ .

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

$f (- x) = - x$

Remove parentheses.

$f (- x) = - x$

Step 2

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

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

$- x$ $\neq$ $x$

Since $- x$ $\neq$ $x$ , 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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Multiply $- 1$ by $x$ .

$- f (x) = - x$

Since $- x = - x$ , the function is odd.

The function is odd

Step 4