https://file.aiquickdraw.com/mathbot/file/1727577806239n3a2oj51.jpg

To determine where the function is increasing or decreasing, let's analyze the graph.

### Key observations from the graph:
1. **Decreasing Intervals:**
   - The function decreases from \( x = -\infty \) to approximately \( x = -1 \). The slope is negative in this region, indicating a decreasing trend.
   - It also decreases between \( x = 1 \) and \( x = 3 \), as the graph slopes downward in this interval.

2. **Increasing Intervals:**
   - The function increases between approximately \( x = -1 \) and \( x = 1 \).
   - The function starts increasing again after \( x = 3 \) and continues increasing toward \( x = \infty \).

### Conclusion:
- **Decreasing intervals**: \( (-\infty, -1) \cup (1, 3) \)
- **Increasing intervals**: \( (-1, 1) \cup (3, \infty) \)

Would you like a detailed explanation of why these intervals are identified as increasing or decreasing?

Here are 5 related questions:
1. How do you find critical points from a graph?
2. What is the significance of inflection points in a function's graph?
3. How can we determine if a function is increasing or decreasing using calculus?
4. What role do local maxima and minima play in determining intervals of increase and decrease?
5. How do changes in the concavity of a graph affect its shape?

**Tip:** To find where a function increases or decreases without a graph, take the derivative and determine where it's positive (increasing) or negative (decreasing).

Identify the open intervals on which the graph of the function is increasing or decreasing. Assume that the graph extends past what is shown. Note: Use the letter U for union. To enter ∞, type infinity.

Analyze the open intervals where the graph of a function increases or decreases. This problem involves understanding graph analysis, critical points, and the first derivative test. Suitable for calculus students in Grades 11-12.

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