To determine the domain of the given function, we need to identify all the possible [tex]\( x \)[/tex]-values from the given table. The domain of a function consists of all the input values for which the function is defined.
Looking at the provided table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-6 & -7 \\
\hline
-1 & 1 \\
\hline
0 & 9 \\
\hline
3 & -2 \\
\hline
\end{tabular}
\][/tex]
we can see the [tex]\( x \)[/tex]-values listed are:
- [tex]\( x = -6 \)[/tex]
- [tex]\( x = -1 \)[/tex]
- [tex]\( x = 0 \)[/tex]
- [tex]\( x = 3 \)[/tex]
These [tex]\( x \)[/tex]-values form the domain of the function.
Thus, the domain of the given function is [tex]\(\{x \mid x = -6, -1, 0, 3\}\)[/tex].
Among the options given:
1. [tex]\(\{x \mid x = -6, -1, 0, 3\}\)[/tex] (Correct)
2. [tex]\(\{y \mid y = -7, -2, 1, 9\}\)[/tex]
3. [tex]\(\{x \mid x = -7, -6, -2, -1, 0, 1, 3, 9\}\)[/tex]
4. [tex]\(\{y \mid y = -7, -6, -2, -1, 0, 1, 3, 9\}\)[/tex]
The correct option is:
[tex]\[
\{x \mid x = -6, -1, 0, 3\}
\][/tex]
