To determine the value of [tex]\( f(5) \)[/tex] from the given table, we simply need to identify the row where [tex]\( x = 5 \)[/tex] and then note the corresponding [tex]\( f(x) \)[/tex] value in that row.
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:
- 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]
Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\( -8 \)[/tex].
Among the provided options:
- [tex]\(-8\)[/tex]
- [tex]\(-1\)[/tex]
- [tex]\(1\)[/tex]
- [tex]\(8\)[/tex]
The correct answer is [tex]\(\boxed{-8}\)[/tex].
