How do you calculate a range in mathematics?

Answer 1

Well...

When you define a function, you're supposed to give it's domain and a set containing it's range with the definition.

Sometimes these are implicit.

For example, for the function square root, one assumes that the domain is the positive real numbers.

The range is then also the positive real numbers.

Generally, the easyest way to do it for an easy function is to draw a picture.

If you're working with real to real functions, you just have to break the function into continuous pieces, and find the maximum and minimum of each piece. The range is then the union of all the intervals between the maxima and minima (it can be open intervals if the function tends asymptotically to it's maxima or minima without reaching them)