I would like to create the following function:
It should approximate a function `func[x]` by piecewise polynomial interpolations, splitting the approximate function in `n` different polynomials, from `xMin` to `xMax`.

    autoPiecewiseApproximation[func[x],{xMin,xMax,n}]

Example: the square root function 

For instance for two subdivisons `n = 2` and `xMin = 0`, `xMax = 1`, the function would automatically generate this:

    m = Piecewise[{{Fit[
         Table[{x, Sqrt[x]}, {x, 0, 0.5, .01}], {1, x, x^2, E^x}, x] , 
        0 <= x <= 0.5}, {Fit[
         Table[{x, Sqrt[x]}, {x, 0.5, 1, .01}], {1, x, x^2, E^x}, x] , 
        0.5 < x <= 1}}]

Anyone knows how to do this correctly ?