Problem 1. In this problem, you will show that the truncated power basis functions, shown below, represent a basis for a cubic spline with one knot. 331(3) = 1, 312(59): 1': 313(3) = 332: 154(33): 33: ital-'3) = (3? (fl:- In other words, you will show that a function of the form fix} = n + {3133' + 3232 + 33173 + {11(3 (f): is indeed a cubic regression spline, regardless of the values of g, ,61,g,,63, :34. Follow the following steps. a. Find a cubic polynomial f1(f} 2 I'll + 513': + (31332 + {1353 such that f[$} = f1[:r) for all a: <_i :5. express b1 all in terms of g ll b. find a cubic polynomial mm a2 dzr that fix for expfbss ill nueamm- you have now establish r is piecewise polynomial. c. show.r f1 fgf x continuous at show f f. e. .5. therefore indeed spline>