# Introduction to Functions

There are many situations in science, business and mathematics where there is a correspondence between two quantities. This correspondence can be described either by a formula, or by a table or by a graph and then recorded as ordered pairs.

The formula y = x2 describes a correspondence between a number and its square.
 Number Square (x) (x2) (1) (1) (2) (4) (3) (9)
The table below describes the relation between the weight of parcel and the postage for it.
 Weight (in gm) Postage (in Rs) 0-100 5 100-200 7 200-300 8 300-400 10 400-500 12
The graph below describes the relation between price of wheat and demand of wheat.
In each of the above illustrations, a correspondence or a rule determines a set of ordered pairs.
Thus a function is a special type relation in which every element of the domain is mapped to one and only one element in the codomain.

Definition: A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in B.