How to avoid asymptotes when I ListPlot a table of data using Mathematica?

Question

I am plotting a table of data using ListPlot in Mathematica. I notice that there are a few asymptotes on the graph which I do not want it to be plotted (i.e. the straight lines between the curves). What should I do to remove the straight lines?

Answer 1

A method from Mark McClure's post here: How to annotate multiple datasets in ListPlots

t = Table[Tan[i], {i, -Pi, Pi, .01}];
plot = ListLinePlot[t];
DeleteCases[plot, Line[_?(Length[#] < 4 &)], Infinity]

Answer 2

Perhaps:

t = Table[Tan[i], {i, -Pi, Pi, .01}];
ListPlot[#, Joined -> True] & /@ {t, t /. x_ /; Abs@x > 10 -> None}

Edit

More robust:

t = Table[Tan[i], {i, -Pi, Pi, .01}];
ao = AbsoluteOptions[ListPlot[t, Joined -> True],PlotRange]/. {_ -> {_,x_}} ->x;
ListPlot[t /. x_ /; (x < ao[[1]] || x > ao[[2]]) -> None,  Joined -> True]