Question

Which value can R have so that the set below represents a function? {(R, 0), (7, -1), (-3, 2), (-1, 3), (6, 7), (-8, 4)}

Options:
A. -8
B. -3
C. 5
D. 7

Answer 1

To determine which value R can have so that the set represents a function, we need to check if there are any repeated x-values in the set. If all the x-values are unique, then the set represents a function. The correct option is C. R can take the value 5 so that the set represents a function.

Step-by-step explanation:

A set of ordered pairs represents a function if each input value (x-value) is associated with exactly one output value (y-value). To determine which value R can have so that the set represents a function, we need to check if there are any repeated x-values in the set. If all the x-values are unique, then the set represents a function.

1. First, we can check if the x-values in the set {(R, 0), (7, -1), (-3, 2), (-1, 3), (6, 7), (-8, 4)} are all unique.
2. If R takes the value -8, then it will not be unique since we already have (-8, 4) in the set. Therefore, option A is not correct.
3. If R takes the value -3, then it will not be unique since we already have (-3, 2) in the set. Therefore, option B is not correct.
4. If R takes the value 5, then it will be unique and the set {(5, 0), (7, -1), (-3, 2), (-1, 3), (6, 7), (-8, 4)} will represent a function.
5. If R takes the value 7, then it will not be unique since we already have (7, -1) in the set. Therefore, option D is not correct.

Therefore, the correct option is C. R can take the value 5 so that the set represents a function.