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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]$y$[/tex]) as a function of time in minutes ([tex]$x$[/tex]).

| [tex]$x$[/tex] | [tex]$y$[/tex] |
|-------|-------|
| 0 | 40 |
| 0.5 | 39.25 |
| 1 | 38.5 |
| 1.5 | 37.75 |

What is the range of this function?

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



Answer :

GinnyAnswer
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].

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