Precalculus Examples

$f (x) = | x |$

Step 1

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$x \geq 0$

Step 2

In the piece where $x$ is non-negative, remove the absolute value.

$x$

Step 3

To find the interval for the second piece, find where the inside of the absolute value is negative.

$x < 0$

Step 4

In the piece where $x$ is negative, remove the absolute value and multiply by $- 1$ .

$- x$

Step 5

Write as a piecewise.

$f (x) = {\begin{cases} x & x \geq 0 \\ - x & x < 0 \end{cases}$