To determine the domain and range of the function represented by the given set of ordered pairs [tex]\(\{(-11, 11), (-8, 8), (0, 0), (13, -13)\}\)[/tex], we follow these steps:
1. Extract the Domain:
The domain consists of all the first elements (x-coordinates) in the set of ordered pairs.
- From the ordered pair [tex]\((-11, 11)\)[/tex], the first element is [tex]\(-11\)[/tex].
- From the ordered pair [tex]\((-8, 8)\)[/tex], the first element is [tex]\(-8\)[/tex].
- From the ordered pair [tex]\((0, 0)\)[/tex], the first element is [tex]\(0\)[/tex].
- From the ordered pair [tex]\((13, -13)\)[/tex], the first element is [tex]\(13\)[/tex].
Thus, the domain is [tex]\(\{-11, -8, 0, 13\}\)[/tex].
2. Extract the Range:
The range consists of all the second elements (y-coordinates) in the set of ordered pairs.
- From the ordered pair [tex]\((-11, 11)\)[/tex], the second element is [tex]\(11\)[/tex].
- From the ordered pair [tex]\((-8, 8)\)[/tex], the second element is [tex]\(8\)[/tex].
- From the ordered pair [tex]\((0, 0)\)[/tex], the second element is [tex]\(0\)[/tex].
- From the ordered pair [tex]\((13, -13)\)[/tex], the second element is [tex]\(-13\)[/tex].
Thus, the range is [tex]\(\{-13, 0, 8, 11\}\)[/tex].
Now, we compare these findings with the provided choices:
A.
- Domain: [tex]\(-11 \leq x \leq 13\)[/tex]
- Range: [tex]\(-13 \leq y \leq 11\)[/tex]
B.
- Domain: [tex]\(\{-13, 0, 8, 11\}\)[/tex]
- Range: [tex]\(\{-11, -8, 0, 13\}\)[/tex]
C.
- Domain: [tex]\(-13 \leq x \leq 11\)[/tex]
- Range: [tex]\(-11 \leq y \leq 13\)[/tex]
D.
- Domain: [tex]\(\{-11, -8, 0, 13\}\)[/tex]
- Range: [tex]\(\{-13, 0, 8, 11\}\)[/tex]
From the analysis, it is clear that:
- The domain [tex]\(\{-11, -8, 0, 13\}\)[/tex] matches the domain provided in choice D.
- The range [tex]\(\{-13, 0, 8, 11\}\)[/tex] matches the range provided in choice D.
Therefore, the correct answer is:
D. Domain: [tex]\(\{-11, -8, 0, 13\}\)[/tex]
Range: [tex]\(\{-13, 0, 8, 11\}\)[/tex]
