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Piecewise function generator

   I want to generate a piecewise continuous linear function by giving a 
function, call it F, a list of {x,y} values defining the corners of the 
function.  I can't seem to do it.  Does anyone out there have a quick way 
of doing it?
   F[pts_] := ????
   {(0.72 f-12)/30 /; 20<=f<=50,
   Thanks in advance,

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