Precalculus Examples

$f (x) = 13 - | 4 x |$

Step 1

Simplify each term.

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Step 1.1

Remove non-negative terms from the absolute value.

$f (x) = 13 - (4 | x |)$

Step 1.2

Multiply $4$ by $- 1$ .

$f (x) = 13 - 4 | x |$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = 13 - 4 | - x |$

Step 2.2

Make $- x$ positive.

$f (- x) = 13 - 4 | x |$

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 $13 - 4 | x | = 13 - 4 | x |$ , the function is even.

The function is even

Step 4