To determine which set of ordered pairs could also belong to the same function as the given set [tex]\(\{(1,7),(-3,0),(5,6),(9,4),(2,2)\}\)[/tex], we need to ensure that no [tex]\(x\)[/tex]-values are repeated in the new set of ordered pairs. Here are the steps:
1. Extract the [tex]\(x\)[/tex]-values from the given function:
[tex]\[
\{1, -3, 5, 9, 2\}
\][/tex]
2. Compare each candidate set of ordered pairs to see if any of their [tex]\(x\)[/tex]-values overlap with those from the given function:
- Candidate Set 1: [tex]\(\{(4,7), (3,-6), (-1,5), (0,-3), (-8,4)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(\{4, 3, -1, 0, -8\}\)[/tex]
- There are no [tex]\(x\)[/tex] values common with [tex]\(\{1, -3, 5, 9, 2\}\)[/tex]. Hence, this set does not overlap.
- Candidate Set 2: [tex]\(\{(3,1), (-4,-6), (8,5), (2,-9), (-7,2)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(\{3, -4, 8, 2, -7\}\)[/tex]
- There is an [tex]\(x\)[/tex] value [tex]\(2\)[/tex] that overlaps with the given function.
- Candidate Set 3: [tex]\(\{(3,7), (0,-2), (9,8), (-1,-1), (-6,5)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(\{3, 0, 9, -1, -6\}\)[/tex]
- There is an [tex]\(x\)[/tex] value [tex]\(9\)[/tex] that overlaps with the given function.
- Candidate Set 4: [tex]\(\{(-8,-2), (4,9), (6,-7), (3,0), (2,5)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(\{-8, 4, 6, 3, 2\}\)[/tex]
- There is an [tex]\(x\)[/tex] value [tex]\(2\)[/tex] that overlaps with the given function.
- Candidate Set 5: [tex]\(\{(-6,2), (5,1), (-7,-4), (8,-5), (3,9)\}\)[/tex]
- [tex]\(x\)[/tex]-values: [tex]\(\{-6, 5, -7, 8, 3\}\)[/tex]
- There is an [tex]\(x\)[/tex] value [tex]\(5\)[/tex] that overlaps with the given function.
3. Conclusion:
- The only candidate set that does not have overlapping [tex]\(x\)[/tex]-values with the given function is:
[tex]\[
\{(4, 7), (3, -6), (-1, 5), (0, -3), (-8, 4)\}
\][/tex]
Thus, the set of ordered pairs that could also belong to the given function is:
[tex]\[
\{(4, 7), (3, -6), (-1, 5), (0, -3), (-8, 4)\}
\][/tex]
