1. ## absolute value graphs

How do you graph lyl-lxl=2?

2. Hello, lilmolldoll41!

I had to baby-talk my way through this one.
. . I hope it makes sense . . .

How do you graph: . $|y| - |x| \:=\:2$ ?

We have: . $|y| \:=\:|x| + 2$

First, we consider: . $y \:=\:|x| + 2$

The graph of $y \:= \:|x|$ is a V-shape with its vertex at the origin.

The graph of $y \:=\:|x| + 2$ is the same graph moved up 2 units.
Code:
                  |
\       |       /
\     |     /
\   |   /
\ | /
*
|
------------+------------
|

Now $|y|$ makes the graph symmetric to the x-axis.
. . (Whatever happens above the x-axis also happens below.)

So the "V" is reflected downward and the graph looks like this:
Code:
                  |
\       |       /
\     |     /
\   |   /
\ | /
*
|
------------+------------
|
*
/ | \
/   |   \
/     |     \
/       |       \
|