To determine which value of [tex]\( x \)[/tex] makes [tex]\( f(x) = -3 \)[/tex], let's examine the values of the function [tex]\( f \)[/tex] provided in the table. The table lists the pairs of [tex]\( x \)[/tex] and [tex]\( f(x) \)[/tex] 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] for which [tex]\( f(x) = -3 \)[/tex].
Let's look at each pair:
- 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].
It is clear from the table that when [tex]\( x = -7 \)[/tex], [tex]\( f(x) \)[/tex] equals [tex]\( -3 \)[/tex].
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = -3 \)[/tex] is [tex]\( \boxed{-7} \)[/tex].
