Sure, let's find the range of the given function based on the table provided. The table shows a set of input-output pairs (x, y). The values of [tex]\(y\)[/tex] for each corresponding [tex]\(x\)[/tex] are provided.
Here is the table again for reference:
[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 range of the function consists of all possible output values (y-values) for the given inputs. Let's list down all the y-values from the table:
- 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]
Therefore, the set of y-values is [tex]\(\{9, 0, -7, -1\}\)[/tex].
Next, let's sort this set of y-values in ascending order to match the choices given:
Sorted y-values: [tex]\([-7, -1, 0, 9]\)[/tex]
Thus, 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]
