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.