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Examples

f (x) = x + 2

$f (x) = x + 2$

Step 1

Find

$f (- x)$ .

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Step 1.1

Find

$f (- x)$ by substituting

$- x$ for all occurrence of

$x$ in

$f (x)$ .

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

Step 1.2

Remove parentheses.

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

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

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

$- x + 2$

$\neq$

$x + 2$ , the function is not even.

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

Find

$- f (x)$ .

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Step 3.1.1

Multiply

$x + 2$ by

$- 1$ .

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

Step 3.1.2

Apply the distributive property.

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

Step 3.1.3

Multiply

$- 1$ by

$2$ .

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

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

Step 3.2

Since

$- x + 2$

$\neq$

$- x - 2$ , the function is not odd.

The function is not odd

The function is not odd

Step 4

The function is neither odd nor even

Step 5

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$