Let's analyze the graph of the kids' swimming pool and answer the questions step by step.

Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant.

1. Increasing:

   • From $t = 0$ to $t = 40$ minutes, the depth increases from 0 feet to 4 feet.
   • Interval: $[0, 40]$

2. Constant:

   • From $t = 40$ to $t = 60$ minutes, the depth remains constant at 4 feet.
   • From $t = 100$ to $t = 140$ minutes, the depth remains constant at 3 feet.
   • Intervals: $[40, 60]$ and $[100, 140]$

3. Decreasing:

   • From $t = 60$ to $t = 100$ minutes, the depth decreases from 4 feet to 3 feet.
   • From $t = 140$ to $t = 180$ minutes, the depth decreases from 3 feet to 0 feet.
   • Intervals: $[60, 100]$ and $[140, 180]$

Part B: What are the domain and range of the relation?

1. Domain:

   • The domain is the set of all possible time values for which the depth is defined.
   • Domain: $[0, 180]$ minutes.

2. Range:

   • The range is the set of all possible depth values.
   • Range: $[0, 4]$ feet.

Part C: Does the graph represent a function? Explain your reasoning.

Yes, the graph represents a function. In mathematical terms, a relation is a function if each input (time in minutes) corresponds to exactly one output (depth in feet). In this case, for each value of time between 0 and 180 minutes, there is a unique depth value. Therefore, the graph is a function.

Part D: Write a detailed description of the graph using the real-world scenario and the information from Part A.

The graph titled "Kids' Swimming Pool" illustrates the depth of water in a swimming pool over time. Initially, from 0 to 40 minutes, the depth of the pool increases steadily from 0 feet to 4 feet, indicating the pool is being filled with water. For the next 20 minutes, from 40 to 60 minutes, the depth remains constant at 4 feet, suggesting that the pool is fully filled and no additional water is being added.

From 60 to 100 minutes, the depth decreases gradually from 4 feet to 3 feet, indicating some water is being drained or splashed out. The depth then stays constant at 3 feet from 100 to 140 minutes, implying no significant changes in the water level. Finally, from 140 to 180 minutes, the depth decreases again from 3 feet to 0 feet, showing the pool is being drained completely. The domain of the graph is from 0 to 180 minutes, and the range is from 0 to 4 feet, confirming the pool's depth varies within these limits.

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Would you like more details or have any questions? Here are some questions you might find helpful:

1. How do you determine the intervals of increase, decrease, and constancy in a graph?
2. What methods can be used to find the domain and range of a function?
3. Why is it important to verify if a graph represents a function?
4. How can you interpret real-world scenarios from graphical data?
5. What are some common features to look for in a piecewise linear graph?

Tip: When analyzing graphs, always pay close attention to the axes labels and the units of measurement, as they provide critical context for interpreting the data accurately.