https://file.aiquickdraw.com/mathbot/file/172686572649739ei8yex.jpg

To help with this, I'll analyze the function graph and its behavior to determine the intervals for when it is increasing, decreasing, and constant.

### Observing the Graph:

1. The function is **increasing** when the slope of the graph is positive.
2. The function is **decreasing** when the slope is negative.
3. The function is **constant** when the graph is flat (horizontal).

### Breakdown of the function:

1. From \( x = -4 \) to \( x = -2 \), the graph is **increasing**.
2. From \( x = -2 \) to \( x = 2 \), the graph is **constant**.
3. From \( x = 2 \) to \( x = 4 \), the graph is **decreasing**.

### Answers:

- **Increasing interval**: \((-4, -2)\)
- **Constant interval**: \((-2, 2)\)
- **Decreasing interval**: \((2, 4)\)

These intervals describe the behavior of the function based on the graph provided.

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Would you like more detailed steps on understanding these intervals or have any specific questions?

Here are 5 related questions for further practice:
1. What is the significance of the endpoints in interval notation?
2. How would you describe a function that is always increasing?
3. Can a function have multiple increasing intervals? If so, give an example.
4. What is the relationship between the derivative of a function and its increasing/decreasing behavior?
5. How would you represent the intervals where the function is non-decreasing?

**Tip**: When analyzing graphs, always look for key points where the graph changes direction (slopes) to identify increasing, decreasing, or constant behavior.

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.

Analyze the function to determine its increasing, decreasing, and constant intervals using interval notation. Suitable for Grades 9-11, this solution covers key concepts of function behavior in a graph.

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