From the graph in the first image, we can identify the function's behavior and locate the discontinuities at $x = -4$, $x = -2$, $x = 2$, and $x = 4$. I will now describe the types of discontinuities at each of these points based on the graph:

1. At $x = -4$:
   The function seems to have a removable discontinuity. There is a hole (open circle) at this point, indicating the limit exists, but the function is not defined at $x = -4$.

2. At $x = -2$:
   There is a jump discontinuity. The graph breaks, with a gap between two segments, and the function takes two different values as you approach from the left and the right.

3. At $x = 2$:
   Another removable discontinuity occurs here. The open circle indicates the function has a hole, suggesting the limit exists, but the value is undefined or different at this point.

4. At $x = 4$:
   The function has an infinite discontinuity. The graph shoots upwards on one side and downwards on the other, meaning the function approaches infinity (vertical asymptote) as $x$ approaches 4 from either side.

Let me know if you'd like more detailed explanations or have further questions.

Here are 5 follow-up questions to expand your understanding:

1. How do you calculate limits approaching a point of removable discontinuity?
2. What is the difference between a jump and infinite discontinuity?
3. Why is the function's behavior different at a removable discontinuity compared to a jump discontinuity?
4. Can a function be continuous at a point with a removable discontinuity if we redefine the value at that point?
5. What types of real-world phenomena can be modeled with functions that have discontinuities?

Tip: Removable discontinuities can often be "fixed" by redefining the function at that point, making the function continuous.