what is the range of f(x)=|x-3|+2?
Note that |x-3| >= 0 for all real x
|x-3| >= 0
So Now adding 2 on both sides of equality, we get
|x-3| + 2 >= 0 + 2
So |x-3| + 2 >= 2
f(x) >= 2
HENCE this means that range of function f(x) = |x-3| + 2 is all real numbers which are >= 2
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