To determine which set of ordered pairs does not represent a function, we need to recall the definition of a mathematical function. A function is a relation where each input (or [tex]\(x\)[/tex]-value) corresponds to exactly one output (or [tex]\(y\)[/tex]-value). This means that within a set of ordered pairs, the [tex]\(x\)[/tex]-value should not be repeated with different [tex]\(y\)[/tex]-values.
Let's examine each given set of ordered pairs to check if any set has repeated [tex]\(x\)[/tex]-values with different [tex]\(y\)[/tex]-values:
1. [tex]\(\{(-3, 9), (1, 5), (9, -8), (6, 1)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(-3, 1, 9, 6\)[/tex]
- The [tex]\(x\)[/tex]-values are all unique and not repeated.
2. [tex]\(\{(9, -2), (-3, 7), (0, -4), (-3, 3)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(9, -3, 0, -3\)[/tex]
- Here, the [tex]\(x\)[/tex]-value [tex]\(-3\)[/tex] is repeated, and it corresponds to different [tex]\(y\)[/tex]-values (7 and 3). Therefore, this set does not represent a function.
3. [tex]\(\{(4, -1), (-3, 1), (6, -7), (7, -1)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(4, -3, 6, 7\)[/tex]
- The [tex]\(x\)[/tex]-values are all unique and not repeated.
4. [tex]\(\{(6, -4), (3, 3), (-3, -7), (-2, -4)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(6, 3, -3, -2\)[/tex]
- The [tex]\(x\)[/tex]-values are all unique and not repeated.
After examining all four sets, we can see that the second set, [tex]\(\{(9, -2), (-3, 7), (0, -4), (-3, 3)\}\)[/tex], does not represent a function because it has the [tex]\(x\)[/tex]-value [tex]\(-3\)[/tex] associated with two different [tex]\(y\)[/tex]-values (7 and 3).
Therefore, the set of ordered pairs that does not represent a function is:
[tex]\[\{(9, -2), (-3, 7), (0, -4), (-3, 3)\}\][/tex]
So, the set that does not represent a function is the second one.
