To determine the value of [tex]\( f(-1) \)[/tex] from the given table, we need to locate the [tex]\( y \)[/tex]-value that corresponds to [tex]\( x = -1 \)[/tex]. Let's carefully examine each pair of [tex]\( (x, f(x)) \)[/tex] in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-5 & 4 \\
\hline
-1 & 0 \\
\hline
6 & -1 \\
\hline
9 & -3 \\
\hline
\end{tabular}
\][/tex]
We find [tex]\( x = -1 \)[/tex] in the second row of the table. Looking at the corresponding [tex]\( f(x) \)[/tex] value in this row, we see that [tex]\( f(-1) = 0 \)[/tex].
Thus, the value of [tex]\( f(-1) \)[/tex] is:
[tex]\[
f(-1) = 0
\][/tex]
Therefore, the correct answer is:
[tex]\( f(-1) = 0 \)[/tex].
