https://file.aiquickdraw.com/mathbot/file/1726606684866soqyboh2.jpg

Based on the image provided, the scenario describes a bathtub draining at a rate of 1.5 gallons per minute. The table shows the amount of water remaining in the bathtub (denoted as \( y \)) as a function of time \( x \), where \( x \) is the time in minutes the bathtub has been draining.

The table data is as follows:
- When \( x = 0 \), \( y = 40 \) gallons.
- When \( x = 0.5 \), \( y = 39.25 \) gallons.
- When \( x = 1 \), \( y = 38.5 \) gallons.
- When \( x = 1.5 \), \( y = 37.75 \) gallons.

### Question:
What is the range of this function?

### Analysis:
The function represents a linear decrease in the amount of water over time, as the bathtub drains at a constant rate of 1.5 gallons per minute. The initial amount of water is 40 gallons, and it decreases over time.

The **range** of a function refers to all the possible values that \( y \) can take. From the table, we observe that \( y \) starts at 40 and decreases, but there is no mention of the water stopping at any particular time, so the draining could potentially continue.

### Correct Answer:
The range is all real numbers such that \( 37.75 \leq y \leq 40 \). Since this is a continuous process, and the function is strictly decreasing, \( y \) will continue to decrease from 40, limited by the smallest value shown in the table (37.75 gallons).

Thus, the correct choice is:  
**All real numbers such that \( 37.75 \leq y \leq 40 \)**.

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Would you like further clarification on this solution or any details? Here are five related questions to expand your understanding:

1. How would you write the equation of the function that represents the draining water?
2. What is the domain of this function, based on the information provided?
3. How long will it take for the bathtub to be completely drained, assuming it continues draining at the same rate?
4. Can this situation be modeled as a linear function, and why?
5. What would be the value of \( y \) after 5 minutes of draining?

**Tip:** When analyzing a function, always consider both the domain (input values) and the range (output values) to fully understand its behavior.

What is the range of this function? The table shows the amount of water remaining in the bathtub, y, as a function of time in minutes, x, that it has been draining.

This problem shows how to determine the range of a linear function in the context of a draining bathtub. The bathtub drains at 1.5 gallons per minute, and the problem asks for the range of the function that represents the remaining water after a certain time.

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