This example:

pts = {{0, 0}, {1, 1}, {2, 0}, {3, 2}}; f = BezierFunction[pts] Show[Graphics[{Red, Point[pts], Green, Line[pts]}, Axes -> True], ParametricPlot[f[t], {t, 0, 1}],Graphics[{Blue, Dashed, BezierCurve[pts]}]] 

perfectly works producing

However with

pts = {{0, 0}, {1, 1}, {2, -1}, {3, 0}, {5, 2}, {6, -1}, {7, 3}}; 

it produces

Why do the curves not coincide and how to access BezierFunction for BezierCurve with npts>4?