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Question 1044862: What is the domain and range of f(x) = |x+2|/(x+2) + |x+3|/(x+3)?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! f(x) = |x+2|/(x+2) + |x+3|/(x+3)
The domain is all x except -2 and -3, for there the denominator of one of the terms is 0.
(-oo,-3)U(-3,-2)U(-2,oo)
The range is from -2to +2. Large negative x will make both terms -1. Large positive x will make both terms+1. At x=-3 there is a hole in the function. The value of the denominator is 0, but the value of the term approaching it is 1, and the numerator and the denominator cancel each other out. The same happens at -2. The graphing here doesn't show it clearly, but the function is discontinuous. At -2.5 or any number between -2 and -3, the first term is negative and the second positive, so the function is 0 in that interval.
In summary, from (-oo,-3) the function is -2. From (-3,-2) it is 0, and from (-2,oo) it is 2.
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