The absolute value function is $\"\"$ .

Observe the graph:

There are two translations.

First translation is horizontal translation.

The graph of $\"\"$ is the graph of $\"\"$ translated.

$\"\"$ units right when $\"\"$ , and $\"\"$ units left when $\"\"$ .

Here $\"\"$ .

The graph of $\"\"$ translated $\"\"$ unit to the right.

Second translation is vertical translation.

The graph of $\"\"$ is the graph of $\"\"$ translated.

$\"\"$ units up when $\"\"$ , and $\"\"$ units down when $\"\"$ .

Here $\"\"$ .

The graph of $\"\"$ translated $\"\"$ units down.

The graph of $\"\"$ is the graph of $\"\"$ translated $\"\"$ unit to the right and $\"\"$ units down.

The equation is $\"\"$

$\"\"$ .