Question

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

Answer 1

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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