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Find the intervals on which f is increasing. (Enter your answer using interval notation.)

To determine the intervals on which the function \( f(x) \) is increasing, we should look at the graph and identify where the slope of the curve is positive. 

### Analysis:
1. A function is increasing where its derivative \( f'(x) \) is positive.
2. On the graph, this corresponds to the intervals where the curve is going upwards as you move from left to right.

### Visual Inspection:
- The curve appears to increase in the following intervals:
  - From approximately \( x \approx -1.5 \) to \( x = 0 \).
  - From approximately \( x = 1.5 \) to \( x = 2.5 \).

### Conclusion:
Based on the graph:
- The function \( f(x) \) is increasing on the intervals \((-1.5, 0)\) and \((1.5, 2.5)\).

Thus, the intervals where \( f(x) \) is increasing are:
\[
(-1.5, 0) \cup (1.5, 2.5)
\]

Would you like further details on the analysis or any additional information?

### Related Questions:
1. How can you determine the intervals of decrease using the graph?
2. What is the derivative \( f'(x) \) and how does it relate to increasing and decreasing intervals?
3. How can you find the local maxima and minima from the graph?
4. What are the critical points, and how can you identify them from the graph?
5. Can you determine concavity from this graph? If so, how?
6. How do the intervals of increase and decrease relate to the overall shape of the graph?
7. How would the intervals change if the graph had a different scale?
8. Can you find the exact values of \( x \) where the function changes from increasing to decreasing?

**Tip:** Always check the derivative to confirm intervals of increase and decrease; a positive derivative indicates an increasing function.

Learn how to identify intervals where a function is increasing using calculus. This problem involves analyzing the derivative of the function to determine where it is positive, indicating increasing behavior. Suitable for advanced high school students.

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