Algebra Examples

$f (x) = 7 | x |$

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.

$7 x$

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 $- 1$ .

$7 (- x)$

Step 5

Write as a piecewise.

$f (x) = {\begin{cases} 7 x & x \geq 0 \\ 7 (- x) & x < 0 \end{cases}$

Step 6

Multiply $- 1$ by $7$ .

$f (x) = {\begin{cases} 7 x & x \geq 0 \\ - 7 x & x < 0 \end{cases}$