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

1 Answer
Feb 27, 2017

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 BTony B