Define function in math

Let me define function in math,

Function is defined as follows, considering two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B.
When a relation satisfies this rule, it is called a fuction.

Hence the function calculator sections helps to differentiate relation and a function.

If : A ---> B and a ? A ??> b ? = f(a) ? B is unique. A is domain and B is co domain or we can call it as Range of function f.

Also we can say that f from A to B is a relation and Every Relation from A to B is not a function.

Note: f is a set of ordered pairs , no two of which have the same first coordinate.

I hope the above explanation was useful.