To determine the domain of a function, we need to identify all the possible input values (x-values) for which the function is defined. The table given shows pairs of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & 3 \\
\hline
4 & 4 \\
\hline
6 & 5 \\
\hline
8 & 6 \\
\hline
\end{array}
\][/tex]
We extract the [tex]\( x \)[/tex]-values from the table:
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 4 \)[/tex]
- [tex]\( x = 6 \)[/tex]
- [tex]\( x = 8 \)[/tex]
Collectively, the set of all [tex]\( x \)[/tex]-values given in the table is [tex]\(\{2, 4, 6, 8\}\)[/tex]. So, we conclude that the domain of the function is the set of these [tex]\( x \)[/tex]-values.
Therefore, the correct answer is:
C. [tex]\(\{2, 4, 6, 8\}\)[/tex]
