Precalculus Examples

f (x) = x

$f (x) = x$

Step 1

Find

f (- x)

$f (- x)$ .

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Find

f (- x)

$f (- x)$ by substituting

- x

$- x$ for all occurrence of

x

$x$ in

f (x)

$f (x)$ .

f (- x) = - x

$f (- x) = - x$

Remove parentheses.

f (- x) = - x

$f (- x) = - x$

f (- x) = - x

$f (- x) = - x$

Step 2

A function is even if

f (- x) = f (x)

$f (- x) = f (x)$ .

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Check if

f (- x) = f (x)

$f (- x) = f (x)$ .

- x

$- x$

\neq

$\neq$

x

$x$

Since

- x

$- x$

\neq

$\neq$

x

$x$ , 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)

$f (- x) = - f (x)$ .

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Multiply

- 1

$- 1$ by

x

$x$ .

- f (x) = - x

$- f (x) = - x$

Since

- x = - x

$- x = - x$ , the function is odd.

The function is odd

The function is odd

Step 4

f (x) = x

$f (x) = x$

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

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