To determine which set represents the same relation as the given table, we need to compare each provided set to the data given in the table. The table provides the following pairs:
[tex]\[
\begin{tabular}{|c|c|}
\hline$x$ & $f(x)$ \\
\hline 0 & 5 \\
\hline 4 & 2 \\
\hline 6 & 9 \\
\hline 9 & 10 \\
\hline
\end{tabular}
\][/tex]
This means the relation is comprised of the ordered pairs [tex]\((x, f(x))\)[/tex]:
[tex]\[
\{ (0, 5), (4, 2), (6, 9), (9, 10) \}
\][/tex]
Now let's evaluate each set:
1. [tex]\(\{ (0, 5), (4, 2), (6, 9), (9, 10) \}\)[/tex]:
- This set contains exactly the same ordered pairs as the table ([tex]\( (0, 5), (4, 2), (6, 9), (9, 10) \)[/tex]).
2. [tex]\(\{ (5, 0), (2, 4), (9, 8), (10, 9) \}\)[/tex]:
- This set contains different ordered pairs: the first elements and second elements are swapped compared to those in the table, and their values also differ.
3. [tex]\(\{ 0, 2, 4, 5, 6, 9, 10 \}\)[/tex]:
- This set contains individual numbers but not ordered pairs. Hence, it does not represent the same relation as the table.
4. [tex]\(\{ 2, 5, 9, 10 \}\)[/tex]:
- Similar to Set 3, this set contains individual numbers but not ordered pairs.
From this evaluation, it is clear that only the first set matches the ordered pairs given in the table exactly.
Therefore, the set that represents the same relation as the table is:
[tex]\(\{ (0, 5), (4, 2), (6, 9), (9, 10) \}\)[/tex]
Hence, the correct set is option 1.
