Looking at the problem in the image, we are given ocean temperature data at various depths below sea level for the Gulf of Mexico. The task involves identifying inputs, outputs, and determining the practical domain and range.

a. Identifying Input, Output, and Variables:

• Input (independent variable): Depth below sea level (in meters). This can be represented by the variable $d$.
• Output (dependent variable): Temperature (in degrees Celsius). This can be represented by the variable $T$.

So, the relationship can be written as: $T = f(d)$ Where $T$ is the temperature and $d$ is the depth in meters.

b. Practical Domain and Range:

• Practical Domain (depth): From the table, the depth values range from 0 meters to 3000 meters, so the practical domain is $0 \leq d \leq 3000$.
• Practical Range (temperature): The temperature values range from 4.12°C to 26.693°C, based on the table. Therefore, the practical range is $4.12 \leq T \leq 26.693$.

Final Answer:

• Practical Domain: $0 \leq d \leq 3000$
• Practical Range: $4.12 \leq T \leq 26.693$

Would you like further details on this problem or any additional help?

Here are 5 related questions to extend this topic:

1. How can you model the relationship between depth and temperature using a mathematical function?
2. What other factors might influence ocean temperature besides depth?
3. How could you approximate the rate of temperature change with respect to depth from this data?
4. How would the practical domain change if we measured deeper than 3000 meters?
5. What type of graph would best represent the relationship between temperature and depth?

Tip: Always define your variables and note the relationship between independent and dependent variables clearly when setting up a mathematical model.