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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.

The graph of a function f is shown. Give the intervals of continuity.

Learn how to determine the intervals of continuity from the graph of a function. This problem explores concepts of continuity and discontinuity, including jumps and holes in the function. Suitable for students in Grades 10-12.

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