To find the domain of the function shown in the table, we need to identify all the possible input values (x-values) for the function. The domain consists of all the x-values listed in the table. Let's examine the table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
3 & -4 \\
\hline
5 & -3 \\
\hline
7 & 3 \\
\hline
9 & 4 \\
\hline
\end{tabular}
From the table, we observe that the x-values provided are 3, 5, 7, and 9.
Now let's match these x-values with the given options:
A. [tex]$\{-4,-3,3,4,5,7,9\}$[/tex] - This set includes y-values as well as x-values, so it's not correct.
B. [tex]$\{3,5,7,9\}$[/tex] - This set includes exactly the x-values from the table.
C. [tex]$\{-4,-3,3,4\}$[/tex] - This set includes y-values and does not cover all the x-values, so it's not correct.
D. [tex]$(3,-4),(5,-3),(7,3),(9,4)$[/tex] - This includes ordered pairs (x, y) instead of just the x-values, so it's not correct.
Therefore, the correct answer is:
B. [tex]$\{3, 5, 7, 9\}$[/tex]
