explain this as though you are teaching a 5th grader

Suppose A and Bare sets. " Casual' definition of a function. A function from A to B is a rule which assigns to every element of the set A a uniquely determined element of the set B . Thus, if f: A - B is a function and a is an element of A, there is a unique element BEB assigned to a by means of the function of. We call 6 the image of a and write b=fla) . In other words, given a function f: A- B, every aE A has a unique image fla)EB. This leads to the following Formal definition of a function . A function from A to B is a subset F of AXB satisfying the requirement: VaEA =]!BEB such that ( a, b) EF. Question : What kind of data is a function formally? Answer: A function is data of the form ( A, B, F ), where Aand B are arbitrary sets and F is a subset of AXB satisfying the requirement of the definition above . The set A is called the domain and B is called the codomain of the function. Question: How do the two definitions correspond to each other? Answer : If we understand a function f: A- B as a certain rule ( Def 1 ), We can assign to it its graph F= ( (a, fla) ) / a E A } S A x B . On the other hand, given a graph FC AXB satisfying Def2, we can assign to it the function f: A - B whose value fla) is precisely that BEB with (a, !) EF, for every at A