To determine which list of ordered pairs represents a function, we need to check if each input (first element in the pair) is associated with exactly one output (second element in the pair).
Let's analyze each list:
A. (2, 5), (3, 8), (4, 11), (4, 12)
- In this list, the input 4 is associated with both 11 and 12, violating the rule of each input having exactly one output. Therefore, this list is not a function.
B. (0, 4), (1, 2), (1, 0), (2, 3)
- Here, the input 1 is associated with both 2 and 0, breaking the rule of a single output for each input. Hence, this list is not a function.
C. (3, -2), (2, 1), (3, 4), (4, 7)
- This list is a function because each input is associated with only one output. For example, input 3 is linked to -2 and then to 4, which is permissible in a function.
D. (1, 7), (2, 5), (3, 6), (4, 1)
- This list is also a function as each input has a unique output, adhering to the definition of a function.
Therefore, the lists of ordered pairs that represent functions are:
- C. (3, -2), (2, 1), (3, 4), (4, 7)
- D. (1, 7), (2, 5), (3, 6), (4, 1)
