To find the range of the given function, we will focus on the [tex]\( y \)[/tex]-values provided in the table. The range of a function is the set of all possible [tex]\( y \)[/tex]-values that the function can take.
Given the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 9 \\
\hline
1 & 0 \\
\hline
4 & -7 \\
\hline
6 & -1 \\
\hline
\end{array}
\][/tex]
The corresponding [tex]\( y \)[/tex]-values are:
[tex]\[ 9, 0, -7, -1 \][/tex]
To determine the range, we list these [tex]\( y \)[/tex]-values in ascending order and remove any duplicates if there are any. In this particular case, there are no duplicates. The sorted list of unique [tex]\( y \)[/tex]-values is:
[tex]\[ -7, -1, 0, 9 \][/tex]
Thus, the range of the given function is:
[tex]\[ \{ y \mid y = -7, -1, 0, 9 \} \][/tex]
Among the given options, this corresponds to:
[tex]\[ \{ y \mid y = -7, -1, 0, 9 \} \][/tex]
Therefore, the correct answer is:
[tex]\[ \{ y \mid y = -7, -1, 0, 9 \} \][/tex]
