Answer :
To determine which pairs of tables represent functions that are inverses of each other, we need to ensure that for each pair [tex]\((x, y)\)[/tex] in the first table, there is a corresponding pair [tex]\((y, x)\)[/tex] in the second table. Essentially, if the first function maps [tex]\(x \rightarrow y\)[/tex], the second function should map [tex]\(y \rightarrow x\)[/tex].
We need to compare the columns of each table.
### Verification Process:
1. Pair 1:
- Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & 4 & 0 & -6 & -10 & -14 \\ \hline \end{array} \][/tex]
- Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & -4 & -2 & 0 & 3 & 5 \\ \hline \end{array} \][/tex]
The entries in Table 1 do not map inversely to the entries in Table 2.
2. Pair 2:
- Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & 4 & 0 & -6 & -10 & -14 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 1 do not map inversely to the entries in Table 4.
3. Pair 3:
- Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 3 & 9 \\ \hline y & -14 & -10 & -6 & 0 & 4 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 3 do not map inversely to the entries in Table 4.
4. Pair 4:
- Table 5:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & -4 & 0 & 6 & 10 & 14 \\ \hline \end{array} \][/tex]
- Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & -4 & -2 & 0 & 3 & 5 \\ \hline \end{array} \][/tex]
The entries in Table 5 do not map inversely to the entries in Table 2.
5. Pair 5:
- Table 5:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & -4 & 0 & 6 & 10 & 14 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 5 do not map inversely to the entries in Table 4.
### Conclusion:
After verifying each pair, none of the tables could be used to verify that the functions they represent are inverses of each other. Therefore, the answer is:
[tex]\[ \boxed{\text{None of the pairs}} \][/tex]
We need to compare the columns of each table.
### Verification Process:
1. Pair 1:
- Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & 4 & 0 & -6 & -10 & -14 \\ \hline \end{array} \][/tex]
- Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & -4 & -2 & 0 & 3 & 5 \\ \hline \end{array} \][/tex]
The entries in Table 1 do not map inversely to the entries in Table 2.
2. Pair 2:
- Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & 4 & 0 & -6 & -10 & -14 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 1 do not map inversely to the entries in Table 4.
3. Pair 3:
- Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 3 & 9 \\ \hline y & -14 & -10 & -6 & 0 & 4 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 3 do not map inversely to the entries in Table 4.
4. Pair 4:
- Table 5:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & -4 & 0 & 6 & 10 & 14 \\ \hline \end{array} \][/tex]
- Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & -4 & -2 & 0 & 3 & 5 \\ \hline \end{array} \][/tex]
The entries in Table 5 do not map inversely to the entries in Table 2.
5. Pair 5:
- Table 5:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & 0 & 2 & 4 \\ \hline y & -4 & 0 & 6 & 10 & 14 \\ \hline \end{array} \][/tex]
- Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -14 & -10 & -6 & 0 & 4 \\ \hline y & 4 & 2 & 0 & -3 & -5 \\ \hline \end{array} \][/tex]
The entries in Table 5 do not map inversely to the entries in Table 4.
### Conclusion:
After verifying each pair, none of the tables could be used to verify that the functions they represent are inverses of each other. Therefore, the answer is:
[tex]\[ \boxed{\text{None of the pairs}} \][/tex]
