Precalculus Review

Even and Odd Functions

A function

is said to be even if it satisfies

. For example,

is even. A function

is said to be odd if it satisfies

Cubing function. A function is called a cubing function if

$\displaystyle f(x) = x^3.$

The cubing function is an odd function, symmetric with respect to the origin.

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Cube root function. A function is called a cube root function if

$\displaystyle f(x) = \sqrt[3]{x}.$

The cube root function is an odd function. The implied domain of

consists of the entire real numbers, that is, $D = (-\infty, \infty)$ .

$\includegraphics{lec03d.ps}$

Absolute value function. A function is called an absolute value function if

$\displaystyle f(x) = \vert x\vert = \left\{\begin{array}{cl} x & \quad\mbox{ if $x \ge 0$; } \\ -x & \quad\mbox{ if $x < 0$. } \end{array}\right.$

The absolute value function is an even function, symmetric with respect to the

-axis.

$\includegraphics{lec04a.ps}$