https://file.aiquickdraw.com/mathbot/file/17273045796552ro0ichg.jpg

From the graph provided, we can identify the intervals where the function is increasing, decreasing, or constant by examining the slope between the given points.

### Coordinates from the graph:
- \((-5, 2)\)
- \((-3, -2)\)
- \((1, 2)\)
- \((4, 2)\)
- \((6, -1)\)

### Analyzing the intervals:
1. **Decreasing:** 
   - The graph is decreasing between \((-5, 2)\) and \((-3, -2)\), and also between \((4, 2)\) and \((6, -1)\), because the graph slopes downward between these points.
   - Interval: \((-5, -3)\) and \((4, 6)\).

2. **Increasing:** 
   - The graph is increasing between \((-3, -2)\) and \((1, 2)\), as the graph slopes upward between these points.
   - Interval: \((-3, 1)\).

3. **Constant:** 
   - The graph is constant between \((1, 2)\) and \((4, 2)\), since the graph forms a horizontal line segment at \(y = 2\).
   - Interval: \((1, 4)\).

### Final answer:
- **Increasing:** \((-3, 1)\)
- **Decreasing:** \((-5, -3)\) and \((4, 6)\)
- **Constant:** \((1, 4)\)

Would you like more details or clarification on any of these intervals?

Here are 5 related questions:
1. How can you identify whether a function is increasing or decreasing on a graph?
2. What is the significance of constant intervals in a function?
3. How do critical points relate to the increasing or decreasing behavior of functions?
4. Can a function have more than one increasing or decreasing interval?
5. What is the importance of using interval notation in calculus?

**Tip:** When working with piecewise functions, always check for changes in slope to determine whether the function is increasing, decreasing, or constant.

From the graph, state the intervals where the function is increasing, decreasing, and constant. Use interval notation.

Learn how to analyze a function based on its graph and identify where it is increasing, decreasing, or constant. Understand the intervals using proper interval notation. Suitable for students in Grades 9-12.

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