https://file.aiquickdraw.com/mathbot/file/1726143878055wn8tk6cj.jpg

In this graph of function \( h \), we can observe the following:

- The dashed lines represent asymptotes, which are points where the function is not defined.
- There are breaks or jumps in the graph, indicating points of discontinuity.

### Interval Analysis for Continuity:
1. **From \([-3, 3]\)**:
   - The function appears continuous from \(-3\) to \(2\). However, at \(x = 2\), there is a jump discontinuity (a gap in the graph). Therefore, the function is **not continuous** over the entire interval \([-3, 3]\).

2. **From \([3, 5]\)**:
   - From \(x = 3\) to \(x = 5\), the function is continuous without any breaks or gaps. So, the function **is continuous** over this interval.

Thus, the correct answer is **B**: \([3, 5]\).

Would you like further details or explanations?

Here are 5 related questions to expand on this topic:
1. What are the conditions for a function to be continuous at a point?
2. How do vertical asymptotes affect the continuity of a function?
3. Can a function be continuous at all points except for one? If so, what is it called?
4. What is the difference between removable and non-removable discontinuities?
5. How can the continuity of a piecewise function be evaluated?

**Tip**: When determining the continuity of a function from a graph, focus on any points where the graph is broken or has jumps, as these indicate discontinuities.

Learn how to analyze the continuity of function h by examining the intervals [-3, 3] and [3, 5]. This problem covers key mathematical concepts like continuity, asymptotes, and jump discontinuities. Suitable for students in Grades 9-12.

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