To determine the range of the function, we need to find the set of all possible values for [tex]\( y \)[/tex] given the time [tex]\( x \)[/tex] in minutes that the bathtub has been draining, as shown in the table provided:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 40 \\
\hline
0.5 & 39.25 \\
\hline
1 & 38.5 \\
\hline
1.5 & 37.75 \\
\hline
\end{array}
\][/tex]
1. Identify the Minimum and Maximum Values of [tex]\( y \)[/tex]:
- From the table, the smallest value of [tex]\( y \)[/tex] (minimum) is 37.75.
- The largest value of [tex]\( y \)[/tex] (maximum) is 40.
2. Establish the Range:
- The range is the set of all possible values that [tex]\( y \)[/tex] can take as [tex]\( x \)[/tex] changes.
- According to the data points provided, [tex]\( y \)[/tex] values range from 37.75 to 40.
Therefore, [tex]\( y \)[/tex] can take any value between 37.75 and 40, inclusive.
3. Conclusion:
- The range of the function is all real numbers such that [tex]\( 37.75 \leq y \leq 40 \)[/tex].
So the correct option is:
- All real numbers such that [tex]\( 37.75 \leq y \leq 40 \)[/tex].
