To determine which ordered pair could not be included in the relation to ensure it remains a function, we need to remember that a function is defined as a relation in which each input (or first element of the ordered pair) is associated with exactly one output (or second element of the ordered pair).
If the ordered pair (4, 4) already exists in the relation, adding another pair with the same first element (4) but a different second element would violate the definition of a function. For instance, if we were to add (4, 5) to the relation, then we would have two pairs with the same first element: (4, 4) and (4, 5), which would mean that the input of 4 has two possible outputs (4 and 5).
Thus, if (4, 4) is already part of the function, then including another pair like (4, 5) would not be allowed.
If, however, (4, 4) is not in the relation yet and you want to include it alongside existing pairs, it wouldn't cause any issues unless there's already a pair (4, y) for some y that is not equal to 4.
In summary, without knowing the context or seeing the other pairs in the relation, it is clear that if (4, 4) is present and we try to add (4, y) where y is not equal to 4, it would lead to a violation of the function property. Therefore, (4, 4) cannot have a different second element when the first element is 4, which would cause it to not remain a function. In simpler terms, adding any ordered pair with the first element 4 but a second element different from 4 would violate the function's definition.