Answer:
The relation in the fourth table (last table) represents the function.
Explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
If we carefully observe, we can check that the first three tables have duplicated inputs.
i.e. In tabel 1, x = 0 is repeated. In other words, x = 0 is duplicated.
i.e. In tabel 2, x = 7 is repeated. In other words, x = 7 is duplicated.
i.e. In tabel 3, x = 3 is repeated. In other words, x = 3 is duplicated.
Therefore, the first three tables DO NOT represent a function as we can not have duplicated inputs as there should be only 1 output for each input.
But, if we check the fourth table, it is clear that the fourth table does not have any duplicated input values.
i.e.
x = 14, 18, 1, and 17
Thus, in the fourth table, each input or x-value of the X set has a unique y-value or output of the Y set.
Hence, the relation in the fourth table (last table) represents the function.