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Plot asymptote on graph

Semen Pampam
Posted 4 years ago

Is it possible to plot an asymptote via a command? I have a function, I plotted it, but there is a problem with the asymptotes, how to plot them? I did a search but it was not unsuccessful. 1 screenshot is how my graph should look like, and 2 screenshot is where I am nowenter image description here

Plot[{(2 x^2 - 9)/Sqrt[x^2 - 1]}, {x, -13, 13}, AxesLabel -> {X, Y}, 
 GridLines -> {{1}, None}]

enter image description here
POSTED BY: Semen Pampam
4 Replies
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Hi, here is another - short and simple - approach:

func = (2 x^2 - 9)/Sqrt[x^2 - 1];
asympt = Asymptotic[func, x -> Infinity];
Plot[{func, asympt}, {x, -13, 13}, AxesLabel -> {"X", "Y"}, GridLines -> {{1}, None}, PlotStyle -> {Automatic, Dashed}]

enter image description here
POSTED BY: Henrik Schachner
POSTED BY: Gianluca Gorni
Semen Pampam
Semen Pampam
Posted 4 years ago

Thanks for the help, I'm new to this and found little information for the graphs. I thought there was a special team that draws everything at once.
POSTED BY: Semen Pampam
Rohit Namjoshi
Rohit Namjoshi
Posted 4 years ago

Hi Semen

exp = (2 x^2 - 9)/Sqrt[x^2 - 1];

asymptotes = ResourceFunction["Asymptotes"][exp, x, y]
(* <|"Vertical" -> {{y -> -∞, x -> ±1}}, 
     "Oblique" -> {{y -> -2 x, x -> -∞}, {y -> 2 x, x -> ∞}}|> *)

If you have to do this for many plots, I would write some code to generate line endpoints from asymptotes. Here I just did it manually

epilog = {Dashed, Darker[Green], InfiniteLine[{{-1, -1}, {-1, 1}}], 
  InfiniteLine[{{1, -1}, {1, 1}}], Red, InfiniteLine[{{-1, -2}, {0, 0}}]}

Plot[exp, {x, -13, 13}, AxesLabel -> {"X", "Y"}, Epilog -> epilog]

enter image description here
POSTED BY: Rohit Namjoshi
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