# absolute value graphs

• Nov 1st 2006, 02:35 PM
lilmolldoll41
absolute value graphs
How do you graph lyl-lxl=2?
• Nov 1st 2006, 03:00 PM
Soroban
Hello, lilmolldoll41!

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

Quote:

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

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

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

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

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

```                  |           \      |      /             \    |    /               \  |  /                 \ | /                   *                   |       ------------+------------                   |```

Now \$\displaystyle |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:

```                  |           \      |      /             \    |    /               \  |  /                 \ | /                   *                   |       ------------+------------                   |                   *                 / | \               /  |  \             /    |    \           /      |      \                   |```