##### Function Introduction

The special type of relation is called as a function.

A relation from A to B is called as a function A to B represented as

only if, for each , we can assign a unique element 'b' such that

where a is called Domain element and b is called as range elements.

**Some characteristics of function:**

1. All the elements of the domain must have a unique image in the range.

2. It is not compulsory that all images in Range have a preimage in the domain.

3. A relation is failed to become a function if any element in domain doesn't have an image in the range.

4. A relation is failed to become a function if any element in the domain has more than one image in the range.

**Total Number of function:**

let say |A| = m and |B| = n then the number of function from A to B is