Mathematica truncates my curves

[Barnak]

I'm ploting a simple function (the effective gravitationnal potentiel with angular momentum part) with Mathematica, and I'm getting some truncated curves close to the vertical asymptote located at r = 0 (see the picture below). Of course, this is normal since the function V(r) diverges at r = 0, but why Mathematica is truncating the first two curves that much ? How can I tell it to draw the curves more closely to the left ?

I'm ploting the curves in the range r = 0 to r = 10, so I should get some better extended curves...

What Mathematica command should I add to get better curves ?

 

[Barnak]

Aaah ! I've found it ! Just use ParametricPlot instead of a simple Plot.

See the picture below :