1.2. Relations and Functions

Definition 1.2.2: Function, Domain, and Range

Let A and B be two sets. A function f from A to B is a relation between A and B such that for each a A there is one and only one associated b B. The set A is called the domain of the function, B is called its range.

Often a function is denoted by y = f(x) or simply f(x), indicating the relation { (x,f(x)) }.

Note: James Cranston (cranstonjames123@gmail.com)) pointed out that occasionally the term codomain is used instead of range, in which case the term range denotes the image of the domain under the function f and is a subset of the codomin. We will, however, stick with our defintion of range as the set containing all values f(a) and possibly more elements; we won't use codomain at all.

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