Which of the relations given by the following sets of ordered pairs is a function?
A.{(2, 4), (2, 6), (2, 8), (2, 10), (2, 12)}
B.{(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}C.{(8, 1), (-4, 1), (3, 5), (0, 4), (-1, 2)}D.{(-5, -4), (-4, -3), (-3, -2), (-4, -5), (-2, -1)}



Answer :

B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)} are the sets of ordered pairs which are the relation that is a function.

To determine whether a set of ordered pairs is a function, we need to determine whether each x-value corresponds to only one y-value. In other words, the x-values in the set should be unique and not repeated.   For the set A. {(2, 4), (2, 6), (2, 8), (2, 10), (2, 12)}, we can see that the x-value 2 is repeated multiple times, and thus, it is not a function.  For the set B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}, each x-value is unique and thus, it is a function.   For the set C. {(8, 1), (-4, 1), (3, 5), (0, 4), (-1, 2)}, we can see that the y-value 1 is repeated twice, and thus, it is not a function.  For the set D. {(-5, -4), (-4, -3), (-3, -2), (-4, -5), (-2, -1)}, each x-value is unique and thus, it is a function.  Therefore, the answer is B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}.

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