P[x_, k_] := 1 - x^(k + 1);
Q[x_, k_] :=  (1 - x)^(-k + 1)

For[k = -3; n = 20; gg = {}, 
      k < 4, k++, 
For [i = 0; w = {}, 
        i ≤ n + 1, i++, 
x = 
          i/(n + 1); 
If[k < 0, 
          w = Append[w, {x, Q[x, k]}], 
          w = Append[w, {x, P[x, k]}]]]; 
gg = 
        Append[gg, Graphics[Line[w]]]]

Show[gg, 
      Axes -> Automatic]