Precalculus Examples

$F (x) = \frac{2 x}{| x |}$

Step 1

Find $f (- x)$ .

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Step 1.1

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

$F (- x) = \frac{2 (- x)}{| - x |}$

Step 1.2

Multiply $- 1$ by $2$ .

$F (- x) = \frac{- 2 x}{| - x |}$

Step 1.3

Make $- x$ positive.

$F (- x) = \frac{- 2 x}{| x |}$

Step 1.4

Move the negative in front of the fraction.

$F (- x) = - \frac{2 x}{| x |}$

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 $- \frac{2 x}{| x |}$ $\neq$ $\frac{2 x}{| x |}$ , 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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Step 3.1

Multiply $- 1$ by $\frac{2 x}{| x |}$ .

$- f (x) = - \frac{2 x}{| x |}$

Step 3.2

Since $- \frac{2 x}{| x |} = - \frac{2 x}{| x |}$ , the function is odd.

The function is odd

Step 4