Data Set 2: Here data set 2 from Assignment 6, which has the derivative issue at x=0.0.

Plot[Piecewise[{{2.0*(x^2)^(1/3),x<0},{1.5*x^(1/3),x>= 0}}],{x,-5,5}, PlotRange->All]

Export["C:\\Users\\kfrin\\Desktop\\Data2.dat",Table[{x,Piecewise[{{2.0*(x^2)^(1/3),x<0},{1.5*x^(1/3),x>= 0}}]},{x,-5,5,0.0005}]]

Data Set 3:  Apply the same process that you did for Data Set 1 and Data Set 2 to a function of your choosing, make it interesting!

Temp  =Table[{x,Piecewise[{{2.0*(x^2)^(1/3),x<0},{1.5*x^(1/3),x>= 0}}]},{x,-5,5,0.0005}];

Length[Temp]

The following definition of Temp2 removes the errors in the x-coordinates that we were seeing in the data file.  I just wrapped the x-coordinate in a NumberForm command, allowing 4 digits of decimal precision!

Temp2  =Table[{NumberForm[x,4],Piecewise[{{2.0*(x^2)^(1/3),x<0},{1.5*x^(1/3),x>= 0}}]},{x,-5.0,5.0,0.01}];

Export["C:\\Users\\kfrin\\Desktop\\Data2.dat",N[Temp2,10]]