To determine the range of the relation given in the table, we need to focus on the [tex]\( y \)[/tex]-values because the range of a function or relation is the set of all possible [tex]\( y \)[/tex]-values (outputs).
Here are the given pairs from the table along with their respective [tex]\( y \)[/tex]-values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
\hline
-1 & 2 \\
\hline
0 & 4 \\
\hline
1 & 2 \\
\hline
2 & 0 \\
\hline
\end{array}
\][/tex]
From the table, the [tex]\( y \)[/tex]-values are:
[tex]\[ y = 0, 2, 4, 2, 0 \][/tex]
Notice that some [tex]\( y \)[/tex]-values are repeated. We need the set of unique [tex]\( y \)[/tex]-values to determine the range. So, we list each [tex]\( y \)[/tex]-value without repetition:
[tex]\[ \{0, 2, 4\} \][/tex]
Finally, we can also arrange these values in ascending order to present the range in a standard format:
[tex]\[ \{0, 2, 4\} \][/tex]
Therefore, the range of the relation is:
[tex]\[ \{0, 2, 4\} \][/tex]
