# How do you find the domain and range of #y=-abs(x)+2#?

##### 1 Answer

Domain:

Range:

#### Explanation:

The domain is all numbers that

In this case, there isn't any value that will make

#y# undefined, since there are no fractions with#x# in the denominator or functions with undefined values (#|x|# is defined for all real numbers). Therefore, the domain of this function is all real numbers, or#RR# .

The range is every value that

We know that the range of

#y = |x|# is#y ge 0# , since the absolute value function returns only positive numbers, or 0 if the input is 0.This means that the range of

#y = -|x|# is#y le 0# , since we're taking every value in the range and making it negative.This means that the range of

#y = -|x|+2# is#y le 2# , since we're adding#2# to every value in the range.

Therefore, the domain is

This is what the graph of this function looks like (notice that all values of

graph{y = -(abs(x))+2 [-10, 10, -5, 5]}