To determine the domain and range of the function represented by the given table, follow these steps:
1. Identify the Domain:
- The domain of a function is the set of all possible input values (x-values) that the function can accept.
- From the table, the x-values are [tex]\(-8\)[/tex], [tex]\(-6\)[/tex], [tex]\(-4\)[/tex], [tex]\(-2\)[/tex], and [tex]\(0\)[/tex].
- Therefore, the domain is the set [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex].
2. Identify the Range:
- The range of a function is the set of all possible output values (y-values) that the function can produce.
- From the table, the y-values are [tex]\(2\)[/tex], [tex]\(2\)[/tex], [tex]\(2\)[/tex], [tex]\(2\)[/tex], and [tex]\(2\)[/tex].
- Since all the y-values are the same, the range is simply the set [tex]\(\{2\}\)[/tex].
3. Compare with the Provided Options:
- Option A states: Domain: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex], Range: [tex]\(\{2\}\)[/tex] which matches our findings perfectly.
- Option B states: Domain: [tex]\(-8 \leq x \leq 0\)[/tex], Range: [tex]\(\{2\}\)[/tex]. This describes the domain and range correctly but the domain is not presented as a set of discrete values.
- Option C states: Domain: [tex]\(\{2\}\)[/tex], Range: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex]. This incorrectly switches the domain and the range.
- Option D states: Domain: [tex]\(\{2\}\)[/tex], Range: [tex]\(y \leq 0\)[/tex]. This is also incorrectly formulated.
Given the correct identification and comparison, the appropriate answer is clearly:
A. Domain: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex] Range: [tex]\(\{2\}\)[/tex]
