# How do you write y = |x+5| as a piecewise function?

Jun 11, 2016

$| x + 5 | = x + 5$ if $x \ge - 5$ and

$| x + 5 | = - x - 5$ if $x < - 5$

#### Explanation:

$| a |$ is a split function as

$| a | = a$ if $a \ge 0$ and $| a | = - a$ if $a < 0$

Similarly, we can write $y = | x + 5 |$ as

$| x + 5 | = x + 5$ if $x + 5 \ge 0$ i.e. $x \ge - 5$ and

$| x + 5 | = - x - 5$ if $x + 5 < 0$ i.e. $x < - 5$