Final answer:
Set D does not represent a function because it includes the x-value -5 paired with two different y-values, which violates the definition of a function.
Step-by-step explanation:
To determine which set of ordered pairs does not represent a function, we need to know what defines a function. A function is a relation where every input (x-value) is associated with exactly one output (y-value). This means that in a set of ordered pairs, each x-value must be unique; it cannot be paired with more than one y-value.
- A. {(4, -6), (-5, 5), (-6, 0), (7, 0)}
- B. {(0, -4), (9, 6), (2, 8), (8, 8)}
- C. {(8, -6), (9, -8), (2, 4), (3, -6)}
- D. {(-5, 2), (3, -9), (-1, 8), (-5, 9)}
Set D includes the ordered pairs (-5, 2) and (-5, 9), where the input -5 is associated with two different outputs, 2 and 9. Therefore, Set D does not represent a function because it violates the definition of a function having only one output for each input.