Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine.

What is the domain and range of the function in the graph?

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5
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8
-1
1
-1
-2
-3
-4
-5
-6
-7
-8
t (sec.)
d (depth)
[Graphs generated by this script: setBorder(5); initPicture(-1,8,-8,1);axes(1,1,1,1,1);line([0,-2],[5,0]);text([6,.5],"t (sec.)");text([1.5,-7.5],"d (depth)");]

D:
to

R:
to

To find the domain and range of the function represented by the graph, let's analyze the key components:

### Domain:
The domain refers to all possible values of \( t \) (time in seconds) for which the function is defined. According to the graph:

- The function starts at \( t = 0 \) and ends at \( t = 5 \) seconds.

Thus, the domain of the function is:
\[
\text{Domain} = [0, 5]
\]

### Range:
The range refers to all possible values of \( d \) (depth) that the function takes. According to the graph:

- The depth starts at \( d = -2 \) (submarine is 2 units below the water surface) and rises to \( d = 0 \) (at the water surface).

Thus, the range of the function is:
\[
\text{Range} = [-2, 0]
\]

### Summary:
- **Domain:** \([0, 5]\)
- **Range:** \([-2, 0]\)

Would you like more details or have any questions about this? 

Here are some follow-up questions you might consider:
1. What does it mean for the depth to be negative in this context?
2. How would the graph change if the submarine started deeper in the water?
3. What would the range be if the submarine continued to rise above the water surface?
4. What is the significance of the slope of the line in this graph?
5. How would the domain change if the submarine took longer to ascend?

**Tip:** When analyzing graphs, always pay attention to where the function starts and ends to determine the domain and range accurately.

Explore the domain and range of a function representing the depth of a toy submarine as it ascends from underwater. Understand the mathematical concepts behind domain and range, applicable for Grades 7-9.

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