Some sites say that a function from A to B is a subset of A x B. But A x B is a

Question

Some sites say that a function from A to B is a subset of A x B. But A x B is a set, and a function is a rule, which means that the GRAPH of a function is the one that is the subset of A x B, not the function itself. Unless the graph of the function is the function. But that cannot be true because two functions with the same codomain could have the same graph. Can someone clear up the confusion? What is the difference between the function and its graph in terms OF SET THEORY. NOT THE ACTUAL GRAPHICAL REPRESENTATION OF IT.

Explanation / Answer

Function is y=f(x)
Graph of the function is {(x,y), where y=f(x)}
Let Domain = A and Range = B
Then Graph of a function is a subset of A x B since suppose (x,y) belongs to the graph, this means y B amd x A with the added constraint that y=f(x)

Hope this clears your confusion.

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