What is the range of $-abs(x-1)+2$ ?

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What is the range of $-abs(x-1)+2$ ?

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Answer 1 · 2015-06-11T13:45:15

We first look at $|x-1|$ which is allways $>=0$
So the negative is allways $<=0$

Explanation:

$->-|x-1|<=0->-|x-1|+2<=2$

Since there is no upper limit to $|x-1|$ , there is no lower limit to the equation as a whole, or:
$- oo <-|x-1|+2<=2$
graph{-|x-1|+2 [-14.24, 14.24, -7.12, 7.12]}

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What is the range of $-abs(x-1)+2$ ?

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