To determine the domain and range of the function represented by the set of ordered pairs [tex]\(\{(-12,-5),(-10,5),(10,-5),(12,5)\}\)[/tex], we need to evaluate the [tex]\(x\)[/tex]-values and [tex]\(y\)[/tex]-values separately.
Step-by-Step Solution:
1. Identify the Ordered Pairs:
- The given ordered pairs are [tex]\((-12, -5)\)[/tex], [tex]\((-10, 5)\)[/tex], [tex]\( (10, -5)\)[/tex], [tex]\( (12, 5)\)[/tex].
2. Determine the Domain:
- The domain of the function consists of all the first components of the ordered pairs.
- So, we take the [tex]\(x\)[/tex]-values from the pairs, which are [tex]\(-12\)[/tex], [tex]\(-10\)[/tex], [tex]\(10\)[/tex], and [tex]\(12\)[/tex].
- Therefore, the domain is [tex]\(\{-12, -10, 10, 12\}\)[/tex].
3. Determine the Range:
- The range of the function consists of all the second components of the ordered pairs.
- So, we take the [tex]\(y\)[/tex]-values from the pairs, which are [tex]\(-5\)[/tex], [tex]\(5\)[/tex], [tex]\(-5\)[/tex], and [tex]\(5\)[/tex].
- Since the [tex]\(y\)[/tex]-values [tex]\(-5\)[/tex] and [tex]\(5\)[/tex] repeat, we list each unique [tex]\(y\)[/tex]-value only once.
- Therefore, the range is [tex]\(\{-5, 5\}\)[/tex].
Conclusion:
The domain of the function is [tex]\(\{-12, -10, 10, 12\}\)[/tex] and the range of the function is [tex]\(\{-5, 5\}\)[/tex].
Thus, the correct answer is:
B. Domain: [tex]\(\{-12, -10, 10, 12\}\)[/tex]
Range: [tex]\(\{-5, 5\}\)[/tex]
