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How to do a family of plots?


Experts, I have used the scheme below with ParametricPlot and it worked. 
But with a simple plot it doesn't. It seems clear the plot function is 
not seeing the f variable.  Plot is not getting machine sized numbers, 
etc. Nothing I've tried seems to help.

I'm trying to get plots of p vs L with f as a parameter. Thanks for any 
help, Rob


p[f_,L_]:=(1-f) ArcCos[Exp[-2/L]]

{q,r,y,z}=Plot[p[f,L],{L,0.1,10}]
/.  f->{0.2,0.4,0.6,0.8}


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