The domain of a function is the set of all possible input values for which the function is defined. In this context, the input values (also known as the x-values) are what we are looking at.
Given the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
2 & 3 \\
\hline
4 & 4 \\
\hline
6 & 5 \\
\hline
8 & 6 \\
\hline
\end{tabular}
\][/tex]
we need to identify the x-values provided.
Looking at the table:
- The first row gives us \(x = 2\).
- The second row gives us \(x = 4\).
- The third row gives us \(x = 6\).
- The fourth row gives us \(x = 8\).
Therefore, the domain of the function is the set of these x-values: \{2, 4, 6, 8\}.
Now, let's examine the given options:
A. \(\{2,3,4,5,6,8\}\) - This set includes additional values \(3\) and \(5\), which are not x-values from the table, so this option is incorrect.
B. \(\{2,4,6,8\}\) - This set matches exactly with the x-values in the table, so this option is correct.
C. \((2,3),(4,4),(6,5),(8,6)\) - This is a set of ordered pairs (x, y), not just the x-values, so this option is incorrect.
D. \(\{3,4,5,6\}\) - This set includes the y-values from the table, not the x-values, so this option is incorrect.
Thus, the domain of the function shown in the table is:
[tex]\(\{2, 4, 6, 8\}\)[/tex], which corresponds to option B.
