To determine which relation is a function of [tex]\( x \)[/tex], we need to check that each [tex]\( x \)[/tex] value maps to exactly one [tex]\( y \)[/tex] value. In other words, a function cannot have the same [tex]\( x \)[/tex] value mapping to different [tex]\( y \)[/tex] values.
Let's examine each relation in turn:
### Relation 1:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-1 & 7 \\
\hline
2 & -9 \\
\hline
2 & 8 \\
\hline
3 & -4 \\
\hline
\end{tabular}
\][/tex]
Here, the [tex]\( x \)[/tex]-value 2 maps to both -9 and 8. This violates the rule that each [tex]\( x \)[/tex]-value must map to exactly one [tex]\( y \)[/tex]-value. Therefore, this relation is not a function.
### Relation 2:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-8 & -9 \\
\hline
-8 & 2 \\
\hline
1 & -9 \\
\hline
1 & 2 \\
\hline
\end{tabular}
\][/tex]
Here, the [tex]\( x \)[/tex]-value -8 maps to both -9 and 2, and the [tex]\( x \)[/tex]-value 1 maps to both -9 and 2. Therefore, this relation is not a function.
### Relation 3:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-5 & 1 \\
\hline
-5 & 7 \\
\hline
-5 & -9 \\
\hline
-5 & 2 \\
\hline
\end{tabular}
\][/tex]
Here, the [tex]\( x \)[/tex]-value -5 maps to multiple [tex]\( y \)[/tex]-values (1, 7, -9, 2). Therefore, this relation is not a function.
### Relation 4:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & -1 \\
\hline
-2 & 5 \\
\hline
\end{tabular}
\][/tex]
In this table, the [tex]\( x \)[/tex]-values -3 and -2 each map to exactly one unique [tex]\( y \)[/tex]-value (-1 and 5, respectively). This confirms that each [tex]\( x \)[/tex]-value has a unique [tex]\( y \)[/tex]-value.
Since Relation 4 fulfills the requirement for a function, it is the relation that is a function of [tex]\( x \)[/tex].
Therefore, the answer is:
[tex]\[
\boxed{4}
\][/tex]
