We have a table of values for a function from which we need to determine the domain and range. The table is given as follows:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -8 & -6 & -4 & -2 & 0 \\
\hline
y & 2 & 2 & 2 & 2 & 2 \\
\hline
\end{array}
\][/tex]
Let's analyze this step-by-step.
### Determining the Domain
The domain of a function is the set of all possible input values (x-values). From the table, the x-values are:
[tex]\[
\{-8, -6, -4, -2, 0\}
\][/tex]
### Determining the Range
The range of a function is the set of all possible output values (y-values). From the table, all the y-values are the same:
[tex]\[
\{2, 2, 2, 2, 2\} \implies \{2\}
\][/tex]
### Comparing with Given Options
Next, we compare our findings with the options provided.
- Option A:
- Domain: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex]
- Range: [tex]\(\{2\}\)[/tex]
This matches exactly with our findings.
- Option B:
- Domain: [tex]\(\{2\}\)[/tex]
- Range: [tex]\(y \leq 0\)[/tex]
The domain here does not match our findings. Additionally, the range described does not match the values in the table.
- Option C:
- Domain: [tex]\(-8 \leq x \leq 0\)[/tex]
- Range: [tex]\(\{2\}\)[/tex]
While this can be represented as the interval [tex]\([-8, 0]\)[/tex], the domain is usually listed explicitly with the exact values from the table. Therefore, the usual representation [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex] is more precise.
- Option D:
- Domain: [tex]\(\{2\}\)[/tex]
- Range: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex]
The domain here does not match the given x-values. Additionally, the range described does not match the constant y-value of 2.
Therefore, comparing all options, we see that:
The correct answer is option A.
Domain: [tex]\(\{-8, -6, -4, -2, 0\}\)[/tex]
Range: [tex]\(\{2\}\)[/tex]
