Precalculus Examples

$y = x + 2$

Step 1

Write $y = x + 2$ as a function.

$f (x) = x + 2$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = (- x) + 2$

Step 2.2

Remove parentheses.

$f (- x) = - x + 2$

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 $- x + 2$ $\neq$ $x + 2$ , the function is not even.

The function is not even

Step 4

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

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Step 4.1

Find $- f (x)$ .

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Step 4.1.1

Multiply $x + 2$ by $- 1$ .

$- f (x) = - (x + 2)$

Step 4.1.2

Apply the distributive property.

$- f (x) = - x - 1 \cdot 2$

Step 4.1.3

Multiply $- 1$ by $2$ .

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

Step 4.2

Since $- x + 2$ $\neq$ $- x - 2$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6