## What is a function?

The concept of function is one of the most important in all mathematics. The basic concept is this: every time we have two sets and some kind of association between them that matches every element of the first set with a single element of the second, a function occurs.

The use of functions can be found in many subjects. For example, in a store's rate card, each product corresponds to a certain price. Another example would be the price to be paid on a utility bill, which depends on the amount of energy consumed. Take, for example, the relationship diagram below:

The above relationship is not a function because there is element 1 in set A, which is not associated with any element in set B. Let's look at another case:

The above relationship is not a function either, as there is element 4 in set A, which is associated with more than one element in set B. Now pay attention to the next example:

The above relationship **it's a function**because every element in set A is associated with only one element in set B**.**

**THE**and

**B**, and a relationship between them, we say that this relationship is a

**A to B function**if and only if,

**for all x**

**THE**exist

**a single y**

**B**so that x relates to y. Next: Domain and Image of a Function