# Function

**DEFINITION1:** Let and be two sets and be a relation. If the following two conditions are provided, then the relation is called a “function” with domain and codomain and denoted by or .

1. ,

2. .

Henceforth, when we write , we will consider that “ is a function from to ”.

As is seen from the definition, a function is a relation mapping each element in the domain to a unique element in the codomain. So, the notation is generally used instead of the notations and and read “ maps to ” or “ maps to ”. The notation is read “ of ”. Each element of the domain is called an “argument” and for each in the domain, the corresponding unique element in the codomain is called “the function value at ”, “output for an element ” or “the image ” under the function . The set defined as is called the “image” or the “range” of . Sometimes a function is called a “map” or a “mapping”.