Introduction to Function

In this class, We discuss Introduction to Function.

The reader should have prior knowledge of relations. Click Here.

Function:

Let X and Y be two sets.

A relation F from X to Y is called a function. If for every x ∈ X there is unique y ∈ Y. such that (x, y) ∈ F

Example:

The below diagram shows a function.

In the second diagram, (1, y1) and (1, y2) belong to F.

The second diagram is not a function.

The third diagram is not a function.

Element 5 does not have a mapping. Every element in the domain should have a mapping.

The function is called mapping, transformation, correspondence, and operation.

Example 2:

The diagram below shows a function F: X -> Y

The elements in the set X are called the domain of the function.

The elements in the set Y are called the codomain of the function.

The elements mapped in the set Y are called the range of the function.

Domain = (1, 2, 5)

Codomain = (y1, y2, y8)

Range = (y1, y2)