A relation contains the ordered pairs (3, 8), (6, 10), (9, 12), and (a, b). For which values of a and is the relation a function? . A. = 3 and b = 14
B. a = 6 and b = 12
C. = 9 and b = 9
D. a = ll and = 8

value of a = 11

value of b = 8

Therefore, option D is correct.

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.

Given the ordered pairs of a relation

(3, 8), (6, 10), (9, 12), and (a, b).

Now, we have to choose the ordered pair containing values of 'a' and 'b' such that there is no duplicated or repeated x-value in the domain of a relation.

It is clear that

WE CAN NOT chose a = 3 and b = 14 because then x = 3 would be repeated. Hence, option A is INCORRECT.

WE CAN NOT chose a = 6 and b = 12 because then x = 6 would be repeated. Hence, option B is INCORRECT.

WE CAN NOT chose a = 9 and b = 9 because then x = 9 would be repeated. Hence, option C is INCORRECT.

But, if we choose a = 11 and b = 8, then the relation would be a function because each input or x-value of the X set will have a unique y-value or output of the Y set.

i.e.

(3, 8), (6, 10), (9, 12), (a, b)

(3, 8), (6, 10), (9, 12), (11, 8)

Thus, the ordered pairs (3, 8), (6, 10), (9, 12), (11, 8) represent the function because each input or x-value of the X set will have a unique y-value or output of the Y set.

Hence,

value of a = 11

value of b = 8

Therefore, option D is correct.