To determine the domain and range of the function represented by the set of ordered pairs [tex]\(\{(-11, 11), (-8, 8), (0, 0), (13, -13)\}\)[/tex], we need to follow these steps:
1. Identify the Domain:
- The domain of a function is the set of all possible [tex]\(x\)[/tex]-values (the first elements in the ordered pairs).
- From the given set of ordered pairs, the [tex]\(x\)[/tex]-values are [tex]\(-11\)[/tex], [tex]\(-8\)[/tex], [tex]\(0\)[/tex], and [tex]\(13\)[/tex].
2. Identify the Range:
- The range of a function is the set of all possible [tex]\(y\)[/tex]-values (the second elements in the ordered pairs).
- From the given set of ordered pairs, the [tex]\(y\)[/tex]-values are [tex]\(11\)[/tex], [tex]\(8\)[/tex], [tex]\(0\)[/tex], and [tex]\(-13\)[/tex].
Based on the extracted values:
- The domain is [tex]\({-11, -8, 0, 13}\)[/tex].
- The range is [tex]\({11, 8, 0, -13}\)[/tex].
Next, we need to match these results to the provided options:
A. Domain: [tex]\(\{-11, -8, 0, 13\}\)[/tex]
Range: [tex]\(\{-13, 0, 8, 11\}\)[/tex]
B. Domain: [tex]\(-13 \leq x \leq 11\)[/tex]
Range: [tex]\(-11 \leq y \leq 13\)[/tex]
C. Domain: [tex]\(-11 \leq x \leq 13\)[/tex]
Range: [tex]\(-13 \leq y \leq 11\)[/tex]
D. Domain: [tex]\(\{-13, 0, 8, 11\}\)[/tex]
Range: [tex]\(\{-11, -8, 0, 13\}\)[/tex]
Option A matches our derived domain [tex]\(\{-11, -8, 0, 13\}\)[/tex] and range [tex]\(\{11, 8, 0, -13\}\)[/tex], after rearranging the elements but still containing the same values. Therefore, the correct answer is:
A. Domain: [tex]\(\{-11, -8, 0, 13\}\)[/tex] Range: [tex]\(\{-13, 0, 8, 11\}\)[/tex].
