To determine which of the given sets of ordered pairs represents a function, we start by recalling the definition of a function. A set of ordered pairs represents a function if and only if each input (or x-value) is associated with exactly one output (or y-value). In other words, there should be no repeated x-values with different corresponding y-values.
Let's evaluate each set one by one:
A. \(\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}\)
- The x-values are: \(-12, -15, -5, -12\).
- The x-value \(-12\) repeats with different y-values (\(8\) and \(-8\)).
- Therefore, set A does not represent a function.
B. \(\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}\)
- The x-values are: \(8, -8, 8, -8\).
- The x-value \(8\) repeats with different y-values (\(-9\) and \(-7\)).
- Additionally, the x-value \(-8\) repeats with different y-values (\(-5\) and \(-6\)).
- Therefore, set B does not represent a function.
C. \(\{(13,-3),(13,0),(13,-1),(13,-1)\}\)
- The x-values are: \(13, 13, 13, 13\).
- The x-value \(13\) repeats with different y-values (\(-3\), \(0\), and \(-1\)).
- Therefore, set C does not represent a function.
D. \(\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}\)
- The x-values are: \(-9, -5, -7, -6\).
- All x-values are unique with only one corresponding y-value each.
- Therefore, set D does represent a function.
So, the set of ordered pairs that represents a function is:
D. [tex]\(\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}\)[/tex]
