To determine which set represents the same relation as the table, we need to compare each option with the given table. The table shows the relationship between [tex]\( x \)[/tex] and [tex]\( f(x) \)[/tex]. The table is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 5 \\
\hline
4 & 2 \\
\hline
6 & 9 \\
\hline
9 & 10 \\
\hline
\end{array}
\][/tex]
We need to find a set that matches this relationship.
### Option Analysis
1. Option 1: { (0, 5), (4, 2), (6, 9), (9, 10) }
This set directly consists of the ordered pairs from the table:
- (0, 5)
- (4, 2)
- (6, 9)
- (9, 10)
This matches the table perfectly.
2. Option 2: { (5, 0), (2, 4), (9, 6), (10, 9) }
This set consists of the reverse of the ordered pairs:
- (5, 0) instead of (0, 5)
- (2, 4) instead of (4, 2)
- (9, 6) instead of (6, 9)
- (10, 9) instead of (9, 10)
This does not match the table.
3. Option 3: { 0, 2, 4, 5, 6, 9, 10 }
This set lists individual elements but does not present them as ordered pairs, so it does not represent a relation.
This does not match the table.
4. Option 4: { 2, 5, 9, 10 }
This set includes some of the values from [tex]\( f(x) \)[/tex] but none of the corresponding [tex]\( x \)[/tex] values, and it does not present them as ordered pairs.
This does not match the table.
### Conclusion
The set that represents the same relation as the table is:
[tex]\[
\{(0,5),(4,2),(6,9),(9,10)\}
\][/tex]
This directly corresponds to Option 1, which matches the given table exactly.
