To determine the range of the function representing the amount of water remaining in Raj's bathtub after it has been draining for a certain amount of time, we can analyze the given data.
The table provided shows:
[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]
Here, [tex]\( x \)[/tex] represents the time in minutes and [tex]\( y \)[/tex] represents the amount of water in gallons.
From the table:
- When [tex]\( x = 0 \)[/tex] (no time has passed), [tex]\( y = 40 \)[/tex] gallons. This is the initial amount of water.
- As time increases to [tex]\( x = 0.5 \)[/tex] minutes, [tex]\( y \)[/tex] decreases to 39.25 gallons.
- When [tex]\( x = 1 \)[/tex] minute, [tex]\( y \)[/tex] decreases to 38.5 gallons.
- Finally, at [tex]\( x = 1.5 \)[/tex] minutes, [tex]\( y \)[/tex] is 37.75 gallons.
Since the water continues to drain and the table only shows up to 1.5 minutes, the lowest recorded value of [tex]\( y \)[/tex] is 37.75 gallons. This suggests that the amount of water in the bathtub varies between 37.75 gallons and 40 gallons during the observed time period.
Thus, the range of the function, which represents the possible values of [tex]\( y \)[/tex] (the amount of water remaining in the bathtub), is:
[tex]\[ 37.75 \leq y \leq 40 \][/tex]
So the correct answer is:
All real numbers such that [tex]\( 37.75 \leq y \leq 40 \)[/tex].
