https://file.aiquickdraw.com/mathbot/file/17266906120458s4gslwj.jpg

To determine the intervals on which the graph of the function \( f \) is increasing, we need to observe the sections of the graph where the slope is positive (i.e., the curve is going upward from left to right).

From the graph provided:

1. **First increasing interval**: The function starts increasing after reaching a local minimum near \( x = -8 \) and continues to increase until it reaches a local maximum at \( x = -6 \).
   
   Thus, the first increasing interval is: \( (-8, -6) \).

2. **Second increasing interval**: After reaching another local minimum around \( x = 0 \), the function begins to increase again and continues to increase until it reaches a local maximum near \( x = 5 \).
   
   Therefore, the second increasing interval is: \( (0, 5) \).

### Conclusion
The function is increasing on the intervals:
\[
(-8, -6) \cup (0, 5)
\]

Would you like more details or have any further questions?

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Here are 5 related questions to expand your understanding:
1. How can you determine decreasing intervals on a graph?
2. What is the significance of local minima and maxima in determining increasing and decreasing intervals?
3. How do you find the critical points of a function algebraically?
4. What is the first derivative test and how does it relate to increasing and decreasing intervals?
5. How can concavity of a function affect the shape of its graph?

**Tip:** To find increasing or decreasing intervals algebraically, you can compute the derivative of the function and analyze where it is positive (increasing) or negative (decreasing).

Determine all intervals on which the graph of f is increasing.

Learn how to determine the increasing intervals on a given graph of the function f. The problem involves analyzing the graph visually to identify where the slope is positive, using concepts from calculus and graph analysis. Suitable for students in Grades 10-12.

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