# Thread: TI: How to find holes and asymptotes in graphs?

1. ## 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:
$\displaystyle \frac{(x-4)(x+3)}{(x-4)(x+5)}$

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)

2. Originally Posted by shailen.sobhee
I have 3 questions:

1) There is a "hole" at the point where x=4 in the graph:
$\displaystyle \frac{(x-4)(x+3)}{(x-4)(x+5)}$

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)
There are some things you actually have to be able to do for yourself rather than rely on a calculator to do them for you.

3. ... true. But since we follow pre-defined rules for finding most of these things, you should be able to find something similar (or simply write the calc. program yourself. It's not that hard :P)

4. Originally Posted by shailen.sobhee
I have 3 questions:

1) There is a "hole" at the point where x=4 in the graph:
$\displaystyle \frac{(x-4)(x+3)}{(x-4)(x+5)}$

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?
Here's the graph of $\displaystyle y=\frac{(x-4)(x+3)}{(x-4)(x+5)}$ on my TI-89 Titanium (with a viewing window of [-8,8] x [-4,4])

Now, if you go to the zoom menu and select "ZoomDec"...

You will get this:

Do you notice something different between these two graphs?

--Chris

5. Now I see the "hole". Besides, discontinuity correction should be turned on to see the small gap.

Like bob said, I guess I shall start writing programs. I'm a programmer, asm or basic should be very easy to learn. I'm planning to write an app that can encircle a hole and make it noticeable.

Sometimes, one cannot easy deduce the existence of a hole by looking at the mathematical expression. For instance, what if the expression was in expanded form?

Thanks to all who contributed.

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