To find the range of the relation given in the table, we need to determine all the unique [tex]\( y \)[/tex]-values corresponding to the [tex]\( x \)[/tex]-values provided. Here are the steps to solve the problem:
1. Identify the [tex]\( y \)[/tex]-values from the table:
Given table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-2 & 0 \\
\hline
-1 & 2 \\
\hline
0 & 4 \\
\hline
1 & 2 \\
\hline
2 & 0 \\
\hline
\end{tabular}
\][/tex]
2. List the [tex]\( y \)[/tex]-values:
From the table, the [tex]\( y \)[/tex]-values are [tex]\( 0 \)[/tex], [tex]\( 2 \)[/tex], [tex]\( 4 \)[/tex], [tex]\( 2 \)[/tex], and [tex]\( 0 \)[/tex].
3. Determine the unique [tex]\( y \)[/tex]-values (the range):
The unique [tex]\( y \)[/tex]-values in the list are [tex]\( 0 \)[/tex], [tex]\( 2 \)[/tex], and [tex]\( 4 \)[/tex].
4. List the range:
The range of the relation is the set of these unique [tex]\( y \)[/tex]-values. Therefore, the range is [tex]\( \{0, 2, 4\} \)[/tex].
Given our options, the correct range is:
- [tex]\(\{0, 2, 4\}\)[/tex]
Thus, the range of the relation in the table is [tex]\(\{0, 2, 4\}\)[/tex].
