To determine the value of [tex]\( f(5) \)[/tex], we need to refer to the provided table, which defines the values of the function [tex]\( f \)[/tex] for specific inputs [tex]\( x \)[/tex]. The table is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -2 \\
\hline
-1 & 5 \\
\hline
3 & 4 \\
\hline
5 & -8 \\
\hline
\end{array}
\][/tex]
From the table, we can see the following pairs [tex]\((x, f(x))\)[/tex]:
- When [tex]\( x = -4 \)[/tex], [tex]\( f(x) = -2 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( f(x) = 5 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( f(x) = 4 \)[/tex]
- When [tex]\( x = 5 \)[/tex], [tex]\( f(x) = -8 \)[/tex]
To find [tex]\( f(5) \)[/tex], we look for the row where [tex]\( x = 5 \)[/tex]. According to the table:
[tex]\[ x = 5 \implies f(5) = -8 \][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\(-8\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-8}
\][/tex]
