The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.
A) {(0, 2), (0, 3)}
B) {(2, 3), (3, 2)}
C) {(3, 1), (4, 1)}
D) {(4, 5), (2, 3)}
To determine which of these relations is a function and which is not, we need to check if each x-value in the relation corresponds to only one y-value.
Let's go through each option:
A) {(0, 2), (0, 3)}
In this relation, we have two ordered pairs with the same x-value of 0 but different y-values. Since 0 is associated with both 2 and 3, this relation is NOT a function.
B) {(2, 3), (3, 2)}
In this relation, we have two ordered pairs with different x-values. The x-values 2 and 3 are each associated with different y-values. Therefore, this relation IS a function.
C) {(3, 1), (4, 1)}
In this relation, we have two ordered pairs with different x-values. Both x-values, 3 and 4, are associated with the same y-value of 1. Therefore, this relation IS a function.
D) {(4, 5), (2, 3)}
In this relation, we have two ordered pairs with different x-values. The x-values 2 and 4 are each associated with different y-values. Therefore, this relation IS a function.
Based on our analysis:
A) {(0, 2), (0, 3)} is NOT a function.
B) {(2, 3), (3, 2)} is a function.
C) {(3, 1), (4, 1)} is a function.
D) {(4, 5), (2, 3)} is a function.
So, the correct answer is B) {(2, 3), (3, 2)}. This is the only relation where reversing the components in each ordered pair does not change the corresponding x-values and y-values, and it still remains a function.