https://file.aiquickdraw.com/mathbot/file/1729479488834sdw97jpe.jpg

From the graph shown in the image, the function changes its behavior in terms of increasing and decreasing intervals. To determine these intervals:

1. **Increasing Interval**: The function is increasing where the graph moves upwards as you move from left to right.
   - The function increases between \( x \approx -5 \) to \( x \approx -3 \) and again from \( x \approx 1.5 \) to \( x \approx 4.5 \).

   So, the increasing intervals (in interval notation) would be approximately:
   \[
   (-5, -3) \cup (1.5, 4.5)
   \]

2. **Decreasing Interval**: The function is decreasing where the graph moves downwards as you move from left to right.
   - The function decreases from \( x \approx -3 \) to \( x \approx 1.5 \) and again after \( x \approx 4.5 \).

   So, the decreasing intervals (in interval notation) would be approximately:
   \[
   (-3, 1.5) \cup (4.5, \infty)
   \]

These intervals are approximate based on the graph.

Let me know if you'd like further explanation or have questions. Here are some related questions to deepen understanding:

1. How does one calculate the exact turning points for increasing/decreasing behavior analytically?
2. What are critical points and how do they relate to increasing/decreasing intervals?
3. What is the difference between local maxima and minima in the context of this graph?
4. How can you determine concavity and points of inflection from a graph?
5. How do increasing/decreasing intervals relate to the derivative of the function?

**Tip**: Always check where the derivative of a function is positive (increasing) or negative (decreasing) to confirm the behavior of the graph.

Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Learn how to determine the intervals where a function is increasing or decreasing by analyzing its graph. This problem covers key calculus concepts and is suitable for high school students in Grades 10-12.

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