TI: How to find holes and asymptotes in graphs?

I have 3 questions:

1) There is a "hole" at the point where x=4 in the graph:

However, the hole is not visible when my TI89 Titanium plots the graph. How can I configure my calculator to show the hole?

I have tried all the possible ways of plotting the graphs (dot, line, think, square, etc), but TI always fills it.

Any ideas? Do you know any TI applications that can encircle the hole and make it more conspicuous?

2) Do you know any TI apps that can calculate the period of trigonometric functions?

E.g: 2sin(x)+4cot(0.5x)+3cos(x)=0

3) Are there any TI app that can definite the asymptote of a graph for a specific domain? (lower and upper bounds stated)