Representation of a function

A function

A function is a relation with a property that for each element in the domain there is only one corresponding element in the range or co-domain. Therefore, functions are relations but not all relations are functions.

Representation of a Function

Example 1

Which of the following relations are functions?

Solution

1. It is not a function since 3 and 6 remain unmapped.
2. It is not a function because 2 has two images (5 and 6).
3. It is a function because each of 1, 2, 3 and 4 is connected to exactly one of 5, 6 or 7.

Testing for Functions

If a line parallel to the y-axis is drawn and it passes through two or more points on the graph of the relation, then the relation is not a function. If it passes through only one point, then the relation is a function.

Example 2

Identify each of the following graphs as functions or not.