To determine [tex]\( f(2) \)[/tex] using the given table, we need to find the value of [tex]\( f(x) \)[/tex] that corresponds to [tex]\( x = 2 \)[/tex].
Let's examine the table step by step:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 0 \\
\hline
-1 & 1 \\
\hline
0 & 2 \\
\hline
1 & -2 \\
\hline
2 & -1 \\
\hline
\end{array}
\][/tex]
When [tex]\( x = 2 \)[/tex], the corresponding value of [tex]\( f(x) \)[/tex] is found in the row where [tex]\( x = 2 \)[/tex]. According to the table, when [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -1 \)[/tex].
Thus, the value of [tex]\( f(2) \)[/tex] is [tex]\( -1 \)[/tex].
Therefore, the correct answer is:
d) -1
