To determine whether a set of ordered pairs represents a function, we need to check if each input (the first element of each pair) maps to exactly one output (the second element of each pair). In other words, no two ordered pairs should have the same first component with different second components.
Let's analyze each set of ordered pairs:
A. (3,5), (4,5), (-2,7), (1,-5)
- Inputs: 3, 4, -2, 1
- All of these inputs are unique.
Conclusion: This set of ordered pairs represents a function.
B. (2,-7), (3,-12), (4,-6), (1,5)
- Inputs: 2, 3, 4, 1
- All of these inputs are unique.
Conclusion: This set of ordered pairs represents a function.
C. (3,9), (0,4), (-1,7), (3,-5)
- Inputs: 3, 0, -1
- The input 3 appears more than once: (3,9) and (3,-5) have different outputs.
Conclusion: This set of ordered pairs does not represent a function.
Summary:
- A: Represents a function.
- B: Represents a function.
- C: Does not represent a function.