To determine which value of [tex]\( x \)[/tex] makes [tex]\( f(x) = -3 \)[/tex] for the function represented by the table, we need to look at the values given in the table and see where [tex]\( f(x) = -3 \)[/tex].
The table is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-7 & -3 \\
\hline
-3 & 5 \\
\hline
2 & -4 \\
\hline
4 & -8 \\
\hline
\end{array}
\][/tex]
We need to find the value of [tex]\( x \)[/tex] that corresponds to [tex]\( f(x) = -3 \)[/tex]. Let's go through each row of the table:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(x) = -3 \)[/tex].
- For [tex]\( x = -3 \)[/tex], [tex]\( f(x) = 5 \)[/tex].
- For [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -4 \)[/tex].
- For [tex]\( x = 4 \)[/tex], [tex]\( f(x) = -8 \)[/tex].
From these observations, we see that [tex]\( f(x) = -3 \)[/tex] when [tex]\( x = -7 \)[/tex].
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = -3 \)[/tex] is:
[tex]\[
\boxed{-7}
\][/tex]
