Final answer:
Option A {(-6,5),(-1, -2), (-4,-6), (-9,5)} is the only set where each input value is paired with one unique output value, thereby fulfilling the definition of a function.
Step-by-step explanation:
A function is defined as a relationship between a set of inputs and a set of possible outputs where each input is related to exactly one output. To determine if a set of ordered pairs represents a function, we must ensure that each input value (or x-coordinate) is paired with only one output value (or y-coordinate).
Let's evaluate each option:
- A. {(-6,5),(-1, -2), (-4,-6), (-9,5)} - This set has distinct x-values for each ordered pair, so it represents a function.
- B. {(-4,-4),(-4,8), (-7,1),(9,7)} - Here, the x-value -4 corresponds to two different y-values (-4 and 8), so it does not represent a function.
- C. {(-3, 4), (6,1),(-8,-8), (-8,-5)} - Similarly, the x-value -8 is paired with two different y-values (-8 and -5), so this also does not represent a function.
- D. {(7,9), (0,4),(-2,1),(7,1)} - In this set, the x-value 7 is associated with two different y-values (9 and 1), so this is not a function either.
Thus, the correct answer is the set from option A, as it has no repeated x-values, meaning each input is paired with only one output.