To find the value of [tex]\( f(-2) \)[/tex] from the given table, we need to locate the row where [tex]\( x \)[/tex] is equal to [tex]\(-2\)[/tex] and read the corresponding [tex]\( f(x) \)[/tex] value.
Here's the detailed step-by-step process:
1. Examine the Table:
The given table lists pairs of [tex]\( x \)[/tex] and [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-6 & 3 \\
\hline
-2 & 1 \\
\hline
0 & 4 \\
\hline
3 & -2 \\
\hline
\end{array}
\][/tex]
2. Identify the Desired Value:
We need to find [tex]\( f(x) \)[/tex] when [tex]\( x \)[/tex] is [tex]\(-2\)[/tex].
3. Locate [tex]\( x = -2 \)[/tex]:
Look at the row where [tex]\( x \)[/tex] is [tex]\(-2\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
-2 & 1 \\
\hline
\end{array}
\][/tex]
4. Read the Corresponding [tex]\( f(x) \)[/tex] Value:
The value corresponding to [tex]\( x = -2 \)[/tex] is [tex]\( f(-2) = 1 \)[/tex].
Thus, the value of [tex]\( f(-2) \)[/tex] is
[tex]\[ 1 \][/tex]
Therefore, the correct answer is [tex]\( \boxed{1} \)[/tex].
