To determine which set of ordered pairs represents a function, we need to check the definition of a function. A set of ordered pairs is a function if and only if each input (or first component) corresponds to exactly one output (or second component). In other words, no two ordered pairs should have the same first component (x) with different second components (y).
Let's analyze each set of ordered pairs:
Set A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
- The first components are: [tex]\(9, 12, 0, -9\)[/tex]
- There are no repeating first components.
- This set can represent a function.
Set B: [tex]\(\{(-9, 9), (-9, 12), (-9, 0), (12, -9)\}\)[/tex]
- The first components are: [tex]\(-9, -9, -9, 12\)[/tex]
- The first component [tex]\(-9\)[/tex] repeats with different second components [tex]\((9, 12, 0)\)[/tex].
- This set cannot represent a function.
Set C: [tex]\(\{(0, -9), (14, -9), (0, 9), (-9, 14)\}\)[/tex]
- The first components are: [tex]\(0, 14, 0, -9\)[/tex]
- The first component [tex]\(0\)[/tex] repeats with different second components [tex]\((-9, 9)\)[/tex].
- This set cannot represent a function.
Set D: [tex]\(\{(9, 14), (9, 4), (0, 0), (11, 16)\}\)[/tex]
- The first components are: [tex]\(9, 9, 0, 11\)[/tex]
- The first component [tex]\(9\)[/tex] repeats with different second components [tex]\((14, 4)\)[/tex].
- This set cannot represent a function.
Therefore, the only set that satisfies the criteria for being a function is:
Set A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
Thus, the correct answer is:
A. [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
