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Raj's bathtub is draining at a rate of 1.5 gallons of water per minute. The table shows the amount of water remaining in the bathtub, [tex][tex]$y$[/tex][/tex], as a function of time in minutes, [tex][tex]$x$[/tex][/tex].

\begin{tabular}{|c|c|}
\hline
[tex][tex]$x$[/tex][/tex] & [tex][tex]$y$[/tex][/tex] \\
\hline
0 & 40 \\
\hline
0.5 & 39.25 \\
\hline
1 & 38.5 \\
\hline
1.5 & 37.75 \\
\hline
\end{tabular}

What is the range of this function?

A. all real numbers such that [tex][tex]$y \leq 40$[/tex][/tex]
B. all real numbers such that [tex][tex]$y \geq 0$[/tex][/tex]
C. all real numbers such that [tex][tex]$0 \leq y \leq 40$[/tex][/tex]
D. all real numbers such that [tex][tex]$37.75 \leq y \leq 40$[/tex][/tex]



Answer :

GinnyAnswer
To determine the range of the function that represents the amount of water remaining in Raj's bathtub over time, we first need to look at the given data points:

[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] is the time in minutes, and [tex]\( y \)[/tex] is the amount of water remaining in gallons.

To find the range of the function, we need to identify the minimum and maximum values of [tex]\( y \)[/tex] in the given table. From the table:

- At [tex]\( x = 0 \)[/tex], [tex]\( y = 40 \)[/tex]
- At [tex]\( x = 0.5 \)[/tex], [tex]\( y = 39.25 \)[/tex]
- At [tex]\( x = 1 \)[/tex], [tex]\( y = 38.5 \)[/tex]
- At [tex]\( x = 1.5 \)[/tex], [tex]\( y = 37.75 \)[/tex]

By inspecting these values, we can see:
- The minimum value of [tex]\( y \)[/tex] is 37.75.
- The maximum value of [tex]\( y \)[/tex] is 40.

Therefore, the amount of water [tex]\( y \)[/tex] is between 37.75 gallons and 40 gallons. Thus, the range of the function is:

[tex]\[ \text{all real numbers such that } 37.75 \leq y \leq 40. \][/tex]

In conclusion, the correct answer is:

[tex]\[ \boxed{\text{all real numbers such that } 37.75 \leq y \leq 40} \][/tex]

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