How do you graph #f(x)=abs((x)-1)-(x)#?

1 Answer
Feb 27, 2017

Answer:

See explanation

Explanation:

#color(red)("Identify the critical points and analyse the behaviour at the point and either side")#

#color(blue)("Consider the case where "x<0)#

Then #|x-1|# is the same as positive #x+1#
now subtract the #-(x)# remembering that #x# is negative.
The net result is #y=positive(2x)+1#
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#color(blue)("I will let you figure out "0 < x < 1)#
The graph shows what you should end up with.
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#color(blue)("Consider the case where "x=1)#

#|x-1|=0" so "|x-1|-1=-1#
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#color(blue)("Consider the case where "x>1)#

#|x-1| " is the same as "x-1#

Put it all together

#|x-1|-x" "->" "x-1-x=1#
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Tony B