The domain would always be the set of all real numbers while the range depends on the sign outside the term in the absolute value and the other operations to be evaluated outside the absolute value term.
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What is the domain and range of absolute lxl - 5
The domain can be anything you like, from the whole of the real numbers to just a single value.
the range is a positive real number
A function is a mapping from one set to another. It may be many-to-one or one-to-one. The first of these sets is the domain and the second set is the range. Thus, for each value x in the domain, the function allocates the value f(x) which is a value in the range. For example, if the function is f(x) = x^2 and the domain is the integers in the interval [-2, 2], then the range is the set [0, 1, 4].
Use the function to find the image of each point in the domain. The set of values that you get will be the range. If the function is well behaved, you will not have to try each and every value in the domain.