Question

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

Answer 1

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]}