To determine which set represents the same relation as the given table, we need to convert the table into a set of ordered pairs. Each ordered pair should be in the form [tex]\((x, f(x))\)[/tex], where [tex]\(x\)[/tex] is the first element (from the left column) and [tex]\(f(x)\)[/tex] is the second element (from the right column).
Given the table:
[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]
We can convert this table into the following set of ordered pairs:
[tex]\[
\{(0, 5), (4, 2), (6, 9), (9, 10)\}
\][/tex]
Now let's compare this with the given answer choices:
1. [tex]\(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\)[/tex]
2. [tex]\(\{(5, 0), (2, 4), (9, 6), (10, 9)\}\)[/tex]
3. [tex]\(\{0, 2, 4, 5, 6, 9, 10\}\)[/tex]
4. [tex]\(\{2, 5, 9, 10\}\)[/tex]
- The first set, [tex]\(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\)[/tex], exactly matches the set we derived from the table. This is the correct answer.
- The second set, [tex]\(\{(5, 0), (2, 4), (9, 6), (10, 9)\}\)[/tex], is not a match because the elements are reversed.
- The third set, [tex]\(\{0, 2, 4, 5, 6, 9, 10\}\)[/tex], is just a collection of individual numbers and does not represent ordered pairs.
- The fourth set, [tex]\(\{2, 5, 9, 10\}\)[/tex], is also a collection of numbers from the right column but does not represent ordered pairs.
Thus, the set that represents the same relation as the given table is:
[tex]\[
\{(0, 5), (4, 2), (6, 9), (9, 10)\}
\][/tex]
