SOLUTION: state the intervals where the function is increasing, decreasing, or constant. The function is: f(x)=-1|x-2|+2

Algebra ->  Functions -> SOLUTION: state the intervals where the function is increasing, decreasing, or constant. The function is: f(x)=-1|x-2|+2      Log On


   

Question 948369: state the intervals where the function is increasing, decreasing, or constant.
The function is: f(x)=-1|x-2|+2
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The critical value is at x=2. The function is split to two branches around x=2.

CASE x%3C2:
-1%28abs%28x-2%29%29%2B2
-1%2A%28-1%29%28x-2%29%2B2 because x-2%3C0;
%28x-2%29%2B2
x


CASE x%3E=2:
f%28x%29=-1%28x-2%29%2B2
-x%2B2%2B2
-x%2B4



Definition for f:
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f%28x%29=x if x%3C2 and f is increasing.
f%28x%29=-x%2B4 if x%3E=2 and f is decreasing (see the negative slope).
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Sometimes my work appears to skip a step.
Be aware of this idea: a-b is an expression;
-%28a-b%29=-1%2A%28a-b%29
-1%2Aa-%28-1%29b
-a%2Bb
b-a
-
Shorter, -%28a-b%29=b-a