To determine which set of ordered pairs represents a function, we need to check if each \( x \)-value in the set is associated with exactly one \( y \)-value. In other words, for each unique \( x \)-value, there should be only one corresponding \( y \)-value.
Let's examine each set of ordered pairs:
1. \(\{(2,-2),(1,5),(-2,2),(1,-3),(8,-1)\}\):
- The \( x \)-values are: \( \{2, 1, -2, 1, 8\} \)
- The \( x \)-value 1 appears twice, associated with different \( y \)-values (5 and -3). Thus, this set does not represent a function.
2. \(\{(3,-1),(7,1),(-6,-1),(9,1),(2,-1)\}\):
- The \( x \)-values are: \( \{3, 7, -6, 9, 2\} \)
- All \( x \)-values are unique. This means each \( x \)-value is associated with exactly one \( y \)-value. Therefore, this set represents a function.
3. \(\{(6,8),(5,2),(-2,-5),(1,-3),(-2,9)\}\):
- The \( x \)-values are: \( \{6, 5, -2, 1, -2\} \)
- The \( x \)-value -2 appears twice, associated with different \( y \)-values (-5 and 9). Thus, this set does not represent a function.
4. \(\{(-3,1),(6,3),(-3,2),(-3,-3),(1,-1)\}\):
- The \( x \)-values are: \( \{ -3, 6, -3, -3, 1 \} \)
- The \( x \)-value -3 appears three times, associated with different \( y \)-values (1, 2, and -3). Thus, this set does not represent a function.
Based on this analysis, the set of ordered pairs that represents a function is:
[tex]\[
\{(3,-1),(7,1),(-6,-1),(9,1),(2,-1)\}
\][/tex]
