# How do you graph y=abs(x-4)-6?

Jun 27, 2018

See below

#### Explanation:

Firstly, find the two different absolute value cases, so:

|x-4|=x-4 (when x-4>=0 -> x>=4) and -1(x-4)(when x<4)
|x-4|=x-4 (when x>=4) and 4-x(when x<4)

Sub the two different cases back into the original $y = | x - 4 | - 6$ equation

When $x \ge 4$,
$y = \left(x - 4\right) - 6$
$y = x - 10$

When $x < 4$,
$y = \left(4 - x\right) - 6$
$y = - x - 2$

Now, simply graph the line $y = x - 10$ for the region $x \ge 4$ and graph $y = - x - 2$ for the region $x < 4$

graph{y=|x-4|-6 [-4.96, 15.04, -7.76, 2.24]}