To determine the intervals of continuity from the graph of the function $f(x)$, we need to examine where the function is continuous and where it has discontinuities. A function is continuous at a point if there is no break, hole, or jump at that point.

Observing the graph:

• The function seems to have a discontinuity at $x = -2$ (there is a hole at this point).
• There is also a jump discontinuity at $x = 0$.
• The function is not defined at $x = 2$ (since there is a hole in the graph here).

Intervals of Continuity:

Based on the graph, the function is continuous in the following intervals:

1. From $(-\infty, -2)$, the function is continuous.
2. From $(-2, 0)$, it is continuous (though $f(-2)$ is not defined).
3. From $(0, 2)$, it is continuous.
4. From $(2, \infty)$, it is continuous.

Thus, the intervals of continuity are: $(-\infty, -2) \cup (-2, 0) \cup (0, 2) \cup (2, \infty)$

Would you like further clarification on any specific part of this?

Here are 5 related questions for deeper understanding:

1. What are the different types of discontinuities a function can have?
2. How can you determine if a function is continuous from its equation rather than its graph?
3. What is the definition of a removable discontinuity?
4. How can a function be continuous but not differentiable at a point?
5. How does continuity of a function affect its limits?

Tip: Always check the function's behavior at specific points, including holes, jumps, and asymptotes, to identify discontinuities.