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By definition, it is the set of all real numbers!
(2x+3) / 5 Domain = All Real Numbers Range = All Real Numbers
The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.
The domain of y = -4x is all real numbers.
It could be a subset: for example, for the function y = log(x), the domain is x > 0. There are many functions whose domain is the complex plane.