Let A and B be two nonempty sets. A function f from A to B is rule which associates to each element x of A a unique element of B. The element y is called the image of x under f and we write f(x) = y which is read “f of x equals y”. A is called the domain of f and B is called the codomain of f. The set of all images of the elements of the domain is called the range of  f. The elements x and y are called the independent and dependent variables respectively.

We can visualize a function f by means of a simple diagram as shown in.

Remark. Note that f (x) does not mean f times x. Let us now consider some examples.


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