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

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Answer 1 · 2018-06-27T12:41:56

See below

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]}

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