To determine the range of the function describing the amount of water remaining in Raj's bathtub as it drains, let's follow these steps.
1. Identify the Initial Condition:
- The bathtub has some initial amount of water, which we'll determine based on the given choices. Here, the maximum given value is 40 gallons. For the sake of this problem, we'll assume the bathtub starts with 40 gallons.
2. Determine the Draining Process:
- The bathtub is draining at a rate of 1.5 gallons per minute. Therefore, over time, the amount of water in the bathtub decreases steadily.
3. Define the End Condition:
- When the bathtub is completely drained, the amount of water remaining is 0 gallons.
4. Determine the Range of Possible Values:
- At the beginning (time [tex]\( x = 0 \)[/tex] minutes), the bathtub contains the maximum water amount, which is 40 gallons.
- As time progresses (for [tex]\( x > 0 \)[/tex] minutes), the amount of water in the bathtub decreases.
- The water amount decreases down to 0 gallons when the bathtub is completely drained.
Therefore, the range of the function [tex]\( y \)[/tex], which represents the amount of water remaining in the bathtub after [tex]\( x \)[/tex] minutes, will be from the minimum possible value (0 gallons) to the maximum initial value (40 gallons).
Putting it together, the correct range for the function [tex]\( y \)[/tex] is:
0 gallons [tex]\(\leq y \leq\)[/tex] 40 gallons
So, the correct choice is:
- All real numbers such that [tex]\( 0 \leq y \leq 40 \)[/tex]
