To determine the domain of a function from a given table, we need to identify all the possible values of [tex]\( x \)[/tex] for which the function is defined. The domain consists of the set of input values (or [tex]\( x \)[/tex]-values) shown in the table.
For the table provided:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
3 & 4 \\
\hline
4 & 4 \\
\hline
5 & 2 \\
\hline
6 & 5 \\
\hline
\end{tabular}
\][/tex]
We see that the [tex]\( x \)[/tex]-values available are [tex]\( 3, 4, 5, \)[/tex] and [tex]\( 6 \)[/tex].
Thus, the domain of the function is the set of all these [tex]\( x \)[/tex]-values.
So, the domain of the function is:
[tex]\[
\{3, 4, 5, 6\}
\][/tex]
The correct answer is:
[tex]\[
\text{A. } \{3, 4, 5, 6\}
\][/tex]
