In mathematics, a relation is considered a function if each input (or x-value) is related to exactly one output (or y-value). This means that no x-value is repeated with a different y-value in the set of ordered pairs.
Let's examine each given set of ordered pairs to determine if it represents a function.
1. \(\{(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)\}\)
- Here, the x-value 1 appears twice: once with y-value 5 and once with y-value -3.
- Since an x-value is repeated with different y-values, this set does not represent a function.
2. \(\{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)\}\)
- The x-values are 3, 7, -6, 9, and 2.
- Each x-value is unique and appears only once.
- Since no x-value is repeated, this set represents a function.
3. \(\{(6, 8), (5, 2), (-2, -5), (1, -3), (-2, 9)\}\)
- Here, the x-value -2 appears twice: once with y-value -5 and once with y-value 9.
- Since an x-value is repeated with different y-values, this set does not represent a function.
4. \(\{(-3, 1), (6, 3), (-3, 2), (-3, -3), (1, -1)\}\)
- Here, the x-value -3 appears three times: once with y-value 1, once with y-value 2, and once with y-value -3.
- Since an x-value is repeated with different y-values, this set does not represent a function.
Given our analysis, the only set that satisfies the criteria for being a function is:
[tex]\[
\{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)\}
\][/tex]
Therefore, the set of ordered pairs that represents a function is set 2.
