https://file.aiquickdraw.com/mathbot/file/1727728517939x2gaouv5.jpg

To solve for the practical range of temperatures (T) from the given table, let's first summarize the relevant information from the image.

### Table Extracted:
- **Depth below sea level (meters):** 0, 40, 100, 300, 550, 1000, 2200, 3000
- **Temperature (°C):** 26.693, 26.516, 25.706, 14.574, 7.848, 4.675, 4.073, 4.12

### Solution Steps:

1. **Input/Output Variables:**
   - Input: Depth below sea level (meters), let's denote this as **\(D\)**.
   - Output: Temperature in degrees Celsius (°C), let's denote this as **\(T\)**.

2. **Practical Domain:**
   - The practical domain (given in your writing) for depth is between 0 meters and 3000 meters. Hence, the domain is \( D \in [0, 3000] \).

3. **Practical Range:**
   - To find the practical range of temperatures, we observe the range of temperature values from the table. These values are:
     - Maximum temperature: 26.693°C (at 0 meters)
     - Minimum temperature: 4.073°C (at 2200 meters)
   
   Therefore, the practical range for **\(T\)** is:
   \[
   T \in [4.073, 26.693] \text{ (in degrees Celsius)}
   \]

Would you like a more detailed explanation or have any further questions?

### Related Questions:
1. How does the temperature change as depth increases?
2. What mathematical model could represent the relationship between depth and temperature?
3. Could you interpolate or extrapolate temperatures for depths not listed in the table?
4. How would changes in temperature affect marine life at various depths?
5. How would you find the rate of temperature change with respect to depth?

**Tip:** When dealing with practical domains and ranges, always check for the limits of your variables based on real-world constraints.

Ocean temperatures drop fairly quickly as you descend into the ocean depths. The following table gives average winter temperatures for the Gulf of Mexico with respect to depth. Given the table, identify the input and output and define a variable to represent each. Then, determine the practical domain and range.

Learn how to determine the practical domain and range from ocean temperature data in the Gulf of Mexico. This problem explores the relationship between ocean depth and temperature, suitable for high school students in Grades 9-12.

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