To find the range of the given function, we need to identify the unique y-values presented in the table. The table provided is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-5 & 9 \\
\hline
1 & 0 \\
\hline
4 & -7 \\
\hline
6 & -1 \\
\hline
\end{tabular}
\][/tex]
First, we list all the y-values from the table:
- When [tex]\(x = -5\)[/tex], [tex]\(y = 9\)[/tex]
- When [tex]\(x = 1\)[/tex], [tex]\(y = 0\)[/tex]
- When [tex]\(x = 4\)[/tex], [tex]\(y = -7\)[/tex]
- When [tex]\(x = 6\)[/tex], [tex]\(y = -1\)[/tex]
Now, we note down these y-values:
[tex]\[ 9, 0, -7, -1 \][/tex]
Next, we arrange these y-values in ascending order to form the range:
[tex]\[ -7, -1, 0, 9 \][/tex]
Therefore, the range of the given function is:
[tex]\(\{y \mid y = -7, -1, 0, 9\}\)[/tex]
So, the correct choice is:
[tex]\(\{y \mid y=-7, -1, 0, 9\}\)[/tex]
