A function is defined as a relation in which each input (the first element of each ordered pair) is associated with exactly one output (the second element). This means that no two ordered pairs can have the same first element if they have different second elements.
In the given set of ordered pairs: (-2, 4), (5, 6), (2, 2), (8, -1), (10, 0), we have the first elements -2, 5, 2, 8, and 10.
Now, let's analyze the options to see which ordered pair could NOT be included in the relation:
- (0, 10) - The first element is 0, which is not already present, so it could be included.
- (8, 5) - The first element is 8, which is already present in the relation as (8, -1). Since (8, 5) has a different second element, this pair cannot be included if we want to maintain the definition of a function.
- (4, 4) - The first element is 4, which is not present, so it could be included.
- (7, 3) - The first element is 7, which is also not present, so it could be included.
Therefore, the ordered pair that could NOT be included in the relation to ensure it remains a function is (8, 5).