Final answer:
The value that makes the set of ordered pairs a function is D) 2, as it is the only value not used as an x-value in the set.
Step-by-step explanation:
The question is asking us to determine which value of a makes a given set of ordered pairs a function. In a function, every input (x-value) must have exactly one output (y-value). Looking at the given set of ordered pairs ((-2, 3), (0, 4), (1, 9), (0, 7)), we can see that the input value 0 is associated with two different output values (4 and 7). This means that as it stands, the set is not a function. To make it a function, we would have to remove one of those pairs with an x-value of 0 or choose a value for a that is not already an x-value in the set.
By examining the options provided:
- A) -2 is already used as an x-value paired with 3.
- B) 0 is repeated with two different y-values, so it cannot be chosen to make this set a function.
- C) 1 is also already used as an x-value paired with 9.
- D) 2 is not in the set as an x-value, so adding a pair with an x-value of 2 would not create any duplicate x-values.
Thus, the correct answer is D) 2.