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Use interval notation to indicate where f is continuous.

To determine where the function \( f(x) \) is continuous based on the graph, we can observe any jumps, breaks, or asymptotes.

### Observations from the graph:
- The graph seems to have several points where the function is not continuous.
- There is a clear vertical asymptote at \( x = 0 \), which suggests the function is not defined or has infinite behavior there.
- Additionally, it appears there are discontinuities at other specific points, marked by hollow circles, indicating possible jump discontinuities.

### Conclusion for Continuity:
The function \( f(x) \) is continuous on all intervals where there are no breaks, jumps, or vertical asymptotes.

Based on the graph, \( f(x) \) appears continuous on the following intervals (in interval notation):
- \( (-\infty, -6] \)
- \( (-6, 0) \)
- \( (0, 1) \)
- \( (1, 3] \)
- \( [3, 5] \)

The points where \( f(x) \) is discontinuous:
- At \( x = 0 \) (vertical asymptote)
- Possibly at some discrete points such as \( x = 1 \) and \( x = 3 \) due to potential jumps (hollow circles).

### Let me know if you'd like more details or clarification.

Here are 5 follow-up questions related to continuity and functions:
1. What are the different types of discontinuities that can occur in a function?
2. How do you determine the continuity of a piecewise function?
3. Can you explain the Intermediate Value Theorem in the context of continuity?
4. What does it mean for a function to have a removable discontinuity?
5. How is the concept of limits connected to the continuity of a function?

**Tip:** When analyzing the continuity of a function, pay close attention to both the domain (where the function is defined) and any potential asymptotes or jumps, as these usually indicate discontinuities.

Analyze the continuity of the function f(x) based on the graph provided. Learn how to use interval notation to identify where the function is continuous and recognize points of discontinuity. This problem is ideal for students studying calculus or advanced algebra in Grades 10-12.

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