To determine which function has the specified domain and range, let’s evaluate each given function in turn.
1. First function: [tex]\(\{(-5, 4), (2, 12), (1, -3), (-5, -7), (1, 0)\} \)[/tex]
- Domain: Extract the first elements of each pair (inputs), which are [tex]\(\{-5, 2, 1\}\)[/tex].
- Range: Extract the second elements of each pair (outputs), which are [tex]\(\{4, 12, -3, 0\}\)[/tex].
- The domain [tex]\(\{-5, 2, 1\}\)[/tex] does not match the desired domain [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex].
- The range [tex]\(\{4, 12, -3, 0\}\)[/tex] does not match the desired range [tex]\(\{-5, 1, 2\}\)[/tex].
- Conclusion: This is not the correct function.
2. Second function: [tex]\(\{(-7, -5), (-3, 1), (0, 2), (-4, 5), (3, -1)\}\)[/tex]
- Domain: Extract the first elements [tex]\(\{-7, -3, 0, -4, 3\}\)[/tex].
- Range: Extract the second elements [tex]\(\{-5, 1, 2, 5, -1\}\)[/tex].
- The domain [tex]\(\{-7, -3, 0, -4, 3\}\)[/tex] does not match the desired domain [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex].
- The range [tex]\(\{-5, 1, 2, 5, -1\}\)[/tex] does not match the desired range [tex]\(\{-5, 1, 2\}\)[/tex].
- Conclusion: This is not the correct function.
3. Third function: [tex]\(\{(-7, -5), (-3, 1), (0, 2), (4, 1), (12, 2)\}\)[/tex]
- Domain: Extract the first elements [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex].
- Range: Extract the second elements [tex]\(\{-5, 1, 2\}\)[/tex].
- The domain [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex] matches the desired domain [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex].
- The range [tex]\(\{-5, 1, 2\}\)[/tex] matches the desired range [tex]\(\{-5, 1, 2\}\)[/tex].
- Conclusion: This is the correct function.
4. Fourth function: [tex]\(\{(-7, 12), (-5, 2)\}\)[/tex]
- Domain: Extract the first elements [tex]\(\{-7, -5\}\)[/tex].
- Range: Extract the second elements [tex]\(\{12, 2\}\)[/tex].
- The domain [tex]\(\{-7, -5\}\)[/tex] does not match the desired domain [tex]\(\{-7, -3, 0, 4, 12\}\)[/tex].
- The range [tex]\(\{12, 2\}\)[/tex] does not match the desired range [tex]\(\{-5, 1, 2\}\)[/tex].
- Conclusion: This is not the correct function.
From the above analysis, the third function [tex]\(\{(-7, -5), (-3, 1), (0, 2), (4, 1), (12, 2)\}\)[/tex] has the desired domain and range.
Therefore, the function that meets the criteria is the third function.
