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 = x^{2} describes a correspondence between a number and its square.
Number |
Square |
(x) | (x^{2}) |
(1) | (1) |
(2) | (4) |
(3) | (9) |
Weight |
Postage |
0-100 | 5 |
100-200 | 7 |
200-300 | 8 |
300-400 | 10 |
400-500 | 12 |
In each of the above illustrations, a correspondence or a rule determines a set of ordered pairs.
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.