To determine the range for the given table of values, we need to follow these steps:
1. Identify the function values, [tex]\( f(x) \)[/tex]:
The table presents the following entries:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
5 & 0 \\
\hline
2 & 0 \\
\hline
-1 & 0 \\
\hline
\end{array}
\][/tex]
2. Extract the function values:
The function values [tex]\( f(x) \)[/tex] from the table are:
[tex]\[
\{0, 0, 0\}
\][/tex]
3. Determine the minimum and maximum values:
- The minimum value in the set [tex]\( \{0, 0, 0\} \)[/tex] is [tex]\( 0 \)[/tex].
- The maximum value in the set [tex]\( \{0, 0, 0\} \)[/tex] is also [tex]\( 0 \)[/tex].
4. Determine the range:
The range of a set of function values is given by the interval from the minimum value to the maximum value. For this particular set, both the minimum and maximum values are 0, so the range is:
[tex]\[
[0, 0]
\][/tex]
In conclusion, the range of the function based on the given table is [tex]\( \{0\} \)[/tex]. Therefore, the answer is:
[tex]\[
(0, 0)
\][/tex]
