To determine the range of the given function, we need to focus on the possible [tex]\( y \)[/tex] values listed in the table. Let's go through this step-by-step:
1. Identify the given [tex]\( y \)[/tex] values from 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]
2. Extract the [tex]\( y \)[/tex] values:
- For [tex]\( x = -5 \)[/tex], [tex]\( y = 9 \)[/tex]
- For [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( y = -7 \)[/tex]
- For [tex]\( x = 6 \)[/tex], [tex]\( y = -1 \)[/tex]
3. List all the [tex]\( y \)[/tex] values:
[tex]\[
y = 9, 0, -7, -1
\][/tex]
4. Sort the [tex]\( y \)[/tex] values in ascending order:
[tex]\[
y = -7, -1, 0, 9
\][/tex]
5. Define the range:
The range of the function is the set of all [tex]\( y \)[/tex] values that the function can output.
Therefore, the range of the given function is [tex]\(\{y \mid y = -7, -1, 0, 9\}\)[/tex].
Hence, the correct answer is:
[tex]\[
\{y \mid y = -7, -1, 0, 9\}
\][/tex]
