https://file.aiquickdraw.com/mathbot/file/1729475777653fwlgei29.jpg

The graph in the image appears to be a function with peaks and valleys, indicating where it increases and decreases. Let me break down how to answer the question:

### Identifying Increasing and Decreasing Intervals:

1. **Increasing Intervals:**
   A function is increasing on an interval where the graph moves upwards as you move from left to right. From the graph, it appears to be increasing between:
   - From \(x = -4\) to \(x = -1\)
   - From \(x = 1\) to \(x = 3\)

2. **Decreasing Intervals:**
   A function is decreasing on an interval where the graph moves downwards as you move from left to right. From the graph:
   - From \(x = -\infty\) to \(x = -4\)
   - From \(x = -1\) to \(x = 1\)
   - From \(x = 3\) to \(x = \infty\)

### Final Answer:
- **Increasing on the intervals:** \( (-4, -1) \cup (1, 3) \)
- **Decreasing on the intervals:** \( (-\infty, -4) \cup (-1, 1) \cup (3, \infty) \)

Let me know if you need further details or clarifications!

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Here are five related questions to consider:
1. What is the behavior of the function at its critical points?
2. How do you identify local maxima and minima in a graph?
3. Can a function be constant on an interval? How would that look on a graph?
4. How do the first and second derivatives help in determining increasing and decreasing intervals?
5. How can inflection points affect the increasing/decreasing nature of a function?

**Tip:** When analyzing graphs, always observe where the slope changes from positive to negative (or vice versa) to determine increasing and decreasing intervals.

The function graphed above is increasing on the interval(s) and decreasing on the interval(s).

This math problem focuses on identifying the increasing and decreasing intervals of a graph. Students will use their knowledge of function behavior and critical points, applying concepts from calculus, including the First Derivative Test. Suitable for students in grades 11-12 or early college courses.

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