Which of these relations is a function?

The relation in the fourth table (last table) represents the function.

Step-by-step 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.

21/58.

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$12. that is my answer.