To find the range of the relation shown in your table, we need to extract the possible output values, which are the [tex]\( y \)[/tex]-values. Let's look at the [tex]\( y \)[/tex]-values given in your table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 5 & 10 & 15 \\
\hline
y & 1 & 7 & 9 & 2 \\
\hline
\end{array}
\][/tex]
The [tex]\( y \)[/tex]-values provided are:
[tex]\[ y = 1, 7, 9, 2 \][/tex]
The range of a relation is the set of all different [tex]\( y \)[/tex]-values. To determine this, we will list each unique [tex]\( y \)[/tex]-value from the table. Here we have:
[tex]\[
1, 7, 9, 2
\][/tex]
Thus, the range of the relation consists of these values. Arranging them in a set (and typically we list set elements in ascending order, although it's not required):
[tex]\[
\{1, 2, 7, 9\}
\][/tex]
However, since there is no need to sort in this context, the range can also be presented exactly as we find them:
[tex]\[
\{1, 7, 9, 2\}
\][/tex]
Therefore, the range of the relation is:
[tex]\[ \{1, 7, 9, 2\} \][/tex]
This is the set of all outputs [tex]\( y \)[/tex]-values for the given inputs [tex]\( x \)[/tex].
