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?

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).