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]}