To identify the value of [tex]\( x \)[/tex] such that [tex]\( f(x) = -2 \)[/tex], we need to examine the table and find the row where the function [tex]\( f(x) \)[/tex] equals [tex]\(-2\)[/tex].
The table values are:
[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]
We will check each row one by one to see where [tex]\( f(x) \)[/tex] is equal to [tex]\(-2\)[/tex]:
1. For [tex]\( x = -2 \)[/tex], [tex]\( f(x) = 0 \)[/tex]
2. For [tex]\( x = -1 \)[/tex], [tex]\( f(x) = 1 \)[/tex]
3. For [tex]\( x = 0 \)[/tex], [tex]\( f(x) = 2 \)[/tex]
4. For [tex]\( x = 1 \)[/tex], [tex]\( f(x) = -2 \)[/tex]
5. For [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -1 \)[/tex]
From the table, we see that when [tex]\( x = 1 \)[/tex], the value of [tex]\( f(x) \)[/tex] is [tex]\(-2\)[/tex].
Therefore, the value of [tex]\( x \)[/tex] such that [tex]\( f(x) = -2 \)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
So the correct answer is b) 1.
