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

1 Answer
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>=4,
y=(x-4)-6
y=x-10

When x<4,
y=(4-x)-6
y=-x-2

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

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