To determine the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -3 \)[/tex], we need to carefully analyze the provided table of values.
Here's the table for reference:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -66 \\
\hline
-3 & -29 \\
\hline
-2 & -10 \\
\hline
-1 & -3 \\
\hline
0 & -2 \\
\hline
1 & -1 \\
\hline
2 & 6 \\
\hline
\end{array}
\][/tex]
We are interested in the value of [tex]\( x \)[/tex] where [tex]\( f(x) = -3 \)[/tex].
1. Find [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column of the table.
2. Look at the corresponding value of [tex]\( x \)[/tex] in the same row.
Let's search for [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -66 \\
\hline
-3 & -29 \\
\hline
-2 & -10 \\
\hline
-1 & \mathbf{-3} \\
\hline
0 & -2 \\
\hline
1 & -1 \\
\hline
2 & 6 \\
\hline
\end{array}
\][/tex]
We observe that when [tex]\( f(x) = -3 \)[/tex], the corresponding [tex]\( x \)[/tex] value is [tex]\( -1 \)[/tex].
Thus, the solution is:
[tex]\[
x = -1 \text{ when } f(x) = -3
\][/tex]
Therefore, the correct answer is [tex]\( -1 \)[/tex].
