Question

Which of the following relations describes a function?

A) { (-4, 4), (-1, 1), (-1, 3), (0, 2) }
B) { (0, 2), (1, 3), (2, 0), (2, 4) }
C) { (0, 2), (1, 3), (4, 4), (9, 5) }
D) { (0, 2), (1, 3), (1, 1), (4, 4}

Answer 1

Option C is the only relation that describes a function.

Step-by-step explanation:

To determine which of the given relations describes a function, we need to check if each x-value is paired with only one y-value. A relation is a function if no x-value repeats in the given relation.

In option A, we have (-1, 1) and (-1, 3), which means that the x-value of -1 is paired with two different y-values. Thus, option A is not a function.

In option B, we have (2, 0) and (2, 4), which means that the x-value of 2 is paired with two different y-values. Thus, option B is not a function.

In option C, all x-values are paired with different y-values, so no x-value repeats. Thus, option C is a function.

In option D, we have (1, 3) and (1, 1), which means that the x-value of 1 is paired with two different y-values. Thus, option D is not a function.

Therefore, the only relation that describes a function is option C.