A complex valued function f of the complex variable z is a rule that assigns to each complex number z in a set D one and only one complex number w . We write w = f(z) and call w the image of z under f . The set D is called the domain of f , and the set of all images {w = f(z), z*epsilon*D} is called the range of f . As we saw in section 1.6, the term domain is also used to indicate a connected open set. When speaking about the domain of a function, however, mathematicians mean only the set of points on which the function is defined. This is a distinction worth noting.