Graphing

[shaheer07]

Hi all,

Is there any way to find the asymptotes of your graph like how you can find them in the TI calculators?

Thanks in Advance,
Shaheer

[Helge Gabert]

Not directly in the plot menu (under Fcn), if that is what you mean - - but just use limit in CAS. If your function is already defined (e.g., in F1), you can also use limit(F1(x), x, limit_value, 0 or -1 or 1) . . . etc.

[Han]

(11-24-2014 04:19 AM)shaheer07 Wrote:  Hi all,

Is there any way to find the asymptotes of your graph like how you can find them in the TI calculators?

Thanks in Advance,
Shaheer

In CAS view

If you have a rational function, using partfrac() will give you the "long division" result from which you can then determine oblique asymptotes. For example:

partfrac((x^2+1)/(x-1)) ---> x+1 + 2/(x-1)

So the oblique asymptote would be y=x+1 (just eliminate the rational remainder)

Horizontal asymptoes are found using the limit() function at infinity.

limit(|x|/(x-1),x,+infinity) ---> 1

So y=1 would be one of the horizontal asymptotes

limit(|x|/(x-1),x,-infinity) ---> -1

So y=-1 would be another asymptote.

For finding vertical asymptotes, use the limit() function as Helge suggested.

limit(2/(x-1),x,1,-1) ---> -infinity
limit(2/(x-1),x,1,+1) ---> +infinity

to confirm that x=1 is a vertical asymptote.

In the Function App

Aside from using the limit() function, you can also determine asymptotes from the Function app and the Num view. After plotting the function, you can use the trace option and move the cursor toward where you think a vertical asymptote may be and (depending on your window settings) the vertical asymptotes will show "NaN".

You can also just type in the X value in the keypad (in the plot view) to get the cursor to move to that location immediately).

In the Num view, you will see NaN appear in the output column.

Those are a few ways to find asymptotes. I'm not sure if that's what you were looking for. Is there some specific command or set of actions on the TI calculator (and which model?) that you list so that we may better answer your question?