To identify the inverse relation, we need to swap the \(x\) and \(y\) values in the given tables. Then, we need to check if the resulting set of pairs forms a function. A relation is a function if each input (x-value) maps to exactly one output (y-value).
For the first table:
- Swap the \(x\) and \(y\) values.
- Check if each \(x\) value is unique.
For the second table:
- Swap the \(x\) and \(y\) values.
- Check if each \(x\) value is unique.
For the first table, we have the pairs:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 9 \\
-1 & 3 \\
0 & -4 \\
1 & 8 \\
2 & -6 \\
3 & 3 \\
\hline
\end{array}
\]
Swapping the \(x\) and \(y\) values gives us the inverse relation:
\[
\text{Inverse Relation 1} = \{(9, -2), (3, -1), (-4, 0), (8, 1), (-6, 2), (3, 3)\}
\]
To determine if this inverse relation is a function, we check for unique \(x\) values. The \(x\) values in the inverse relation are:
\[
\{9, 3, -4, 8, -6, 3\}
\]
Since the value \(3\) appears twice, the inverse relation is not a function.
For the second table, we have the pairs:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & -7 \\
1 & 6 \\
0 & 8 \\
1 & -1 \\
2 & 3 \\
3 & 7 \\
\hline
\end{array}
\]
Swapping the \(x\) and \(y\) values gives us the inverse relation:
\[
\text{Inverse Relation 2} = \{(-7, -2), (6, 1), (8, 0), (-1, 1), (3, 2), (7, 3)\}
\]
To determine if this inverse relation is a function, we check for unique \(x\) values. The \(x\) values in the inverse relation are:
\[
\{-7, 6, 8, -1, 3, 7\}
\]
All \(x\) values are unique, so the inverse relation is a function.
For the first table, the inverse relation is not a function. For the second table, the inverse relation is a function. Thus, we conclude:
\[
\boxed{\text{Inverse Relation 1: Not a function, Inverse Relation 2: Function}}
\]
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