To determine the range of the function representing the amount of water remaining in Raj's bathtub, we need to examine the given table and understand how the values change over time. The table indicates the following values:
[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 remaining in the bathtub in gallons. From the table, we observe how the water level decreases with time.
- At [tex]\(x = 0\)[/tex], the water level [tex]\(y\)[/tex] is 40 gallons.
- At [tex]\(x = 0.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 39.25 gallons.
- At [tex]\(x = 1\)[/tex] minute, the water level [tex]\(y\)[/tex] is 38.5 gallons.
- At [tex]\(x = 1.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 37.75 gallons.
To determine the range of this function, we need to identify the minimum and maximum values of [tex]\(y\)[/tex] from the table.
- The minimum value of [tex]\(y\)[/tex] in the given table is 37.75 gallons.
- The maximum value of [tex]\(y\)[/tex] in the given table is 40 gallons.
The range of the function is therefore all real numbers [tex]\(y\)[/tex] such that [tex]\(37.75 \leq y \leq 40\)[/tex].
Thus, the correct answer is:
all real numbers such that [tex]\(37.75 \leq y \leq 40\)[/tex].
