To determine the domain and range of the given function [tex]\(\{(6,-8),(9,3),(-3,5),(1,-6),(5,7)\}\)[/tex], we need to understand what domain and range mean.
1. Domain: The domain of a function is the set of all possible [tex]\(x\)[/tex]-values (inputs) that make the function work.
2. Range: The range of a function is the set of all possible [tex]\(y\)[/tex]-values (outputs) that the function can produce.
Given the function [tex]\(\{(6,-8),(9,3),(-3,5),(1,-6),(5,7)\}\)[/tex], we can list out the [tex]\(x\)[/tex]-values and [tex]\(y\)[/tex]-values separately:
- The [tex]\(x\)[/tex]-values from the ordered pairs are: [tex]\(6, 9, -3, 1, 5\)[/tex]
- The [tex]\(y\)[/tex]-values from the ordered pairs are: [tex]\(-8, 3, 5, -6, 7\)[/tex]
Now, let's organize these values into sets for the domain and range:
- The domain (set of all [tex]\(x\)[/tex]-values) is: [tex]\(\{6, 9, -3, 1, 5\}\)[/tex]
- The range (set of all [tex]\(y\)[/tex]-values) is: [tex]\(\{-8, 3, 5, -6, 7\}\)[/tex]
We can rearrange these in ascending order:
- Domain: [tex]\(\{-3, 1, 5, 6, 9\}\)[/tex]
- Range: [tex]\(\{-8, -6, 3, 5, 7\}\)[/tex]
Therefore, the answer is:
C. Domain: [tex]\(\{-3, 1, 5, 6, 9\}\)[/tex]; Range: [tex]\(\{-8, -6, 3, 5, 7\}\)[/tex]
