Precalculus Examples

$f (x) = 2 | x | - 5$

Step 1

Find $f (- x)$ .

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Step 1.1

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

$f (- x) = 2 | - x | - 5$

Step 1.2

Make $- x$ positive.

$f (- x) = 2 | x | - 5$

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 $2 | x | - 5 = 2 | x | - 5$ , the function is even.

The function is even

Step 3