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The question asks to select all the intervals where the function \( f(x) \) is increasing, based on the graph provided. The graph shows a periodic wave-like function.

### To find where \( f(x) \) is increasing:
A function is increasing when its slope is positive, meaning the curve goes upwards from left to right. We need to identify the regions on the graph where this happens.

Looking at the graph:

1. **Interval from \( -3 < x < -2 \)**: In this region, the graph is going *downward*, not upward, so the function is decreasing, not increasing.
2. **Interval from \( -1 < x < 0 \)**: In this range, the function is *increasing*, as the graph is moving upwards from left to right.
3. **Interval from \( 3.5 < x < 4.5 \)**: In this interval, the graph is also moving upwards, indicating that the function is *increasing*.

### Conclusion:
The correct intervals where the function is increasing are:

- \( -1 < x < 0 \) (Answer B)
- \( 3.5 < x < 4.5 \) (Answer C)

Hence, the answers would be **B** and **C**.

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Do you want further details or have any questions?

Here are 5 questions to explore further:
1. What is the definition of an increasing function?
2. How do we determine if a function is decreasing from a graph?
3. Can a function be increasing and decreasing within the same interval?
4. What are periodic functions, and how do they behave?
5. How can we find the derivative of \( f(x) \) to confirm the intervals of increase?

**Tip:** The slope of a function can be understood by the sign of the derivative—positive for increasing, negative for decreasing.

Selecione todos os intervalos em que f é crescente.

Learn how to identify intervals where a function is increasing based on its graph. This example explores a periodic function and highlights key calculus concepts such as positive slopes and increasing functions. Suitable for high school students (Grades 10-12).

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