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Which function has the following domain and range?

Domain: [tex]\{-7,-3,0,4,12\}[/tex]
Range: [tex]\{-5,1,2\}[/tex]

A. [tex]\{(-5,4),(2,12),(1,-3),(-5,-7),(1,0)\}[/tex]
B. [tex]\{(-7,-5),(-3,1),(0,2),(-4,5),(3,-1)\}[/tex]
C. [tex]\{(4,1),(-3,-5),(12,2),(0,-5),(-7,1)\}[/tex]
D. [tex]\{(-7,12),(-5,2)\}[/tex]

Sagot :

GinnyAnsweridn
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.
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