The range of a function y = f (x) is the set of all possible output values f (x) corresponding to every input x in the domain of f and is denoted as f (A) if A is the domain. For finding the range of a function y = f (x), first of all, find the domain of f.
If the domain consists of finite number of points, then the range consists of set of corresponding f (x) values. If the domain consists of whole real line or real line minus some finite points, then express x in terms of y as x = g(y). The values of y for which g is defined is the required range.
If the domain is a finite interval, find the intervals in which f (x) increases/decreases and then find the extreme values of the function in those intervals. The union of those intervals is the required range.