Plot of various Piecewise and combine

Question

I want to combine plot of four piecewise function for the following for. I have a code with "For", and I do not know which 'Show' can help me.

n = 4;
x[0] = 0;
x[n] = 1;
Do[x[L + 1] = N[x[L] + 1, 1];, {L, 0, 1}]
Subscript[A, 0][x_] = 
         Piecewise[{{1 - (x - x[0])/(x[1] - x[0]), x[0] <= x <= x[1]}}]
            For[k = 0, k < n - 1, k++; 
             Print[Subscript[A, k][x_] = 
               Piecewise[{{(x - x[k - 1])/(x[k] - x[k - 1]), 
                  x[k - 1] <= x <= x[k]}, {1 - (x - x[k])/(x[k + 1] - x[k]), 
                  x[k] <= x <= x[k + 1]}}]]]

Any suggestion?

Answer 1

I think you are trying to do something like the following:

ClearAll[x]
n = 4;
x[0] = 0;
x[n] = 1;
Do[x[L + 1] = x[L] + 1;, {L, 0, 2}];
x /@ {0, 1, 2, 3, 4}

{0, 1, 2, 3, 1}

ClearAll[aa]
aa[0][y_] :=  Piecewise[{{1 - (y - x[0])/(x[1] - x[0]), x[0] <= y <= x[1]}}]
aa[k_][y_] := Piecewise[{{(y - x[k - 1])/(x[k] - x[k - 1]), x[k - 1] <= y <= x[k]}, 
    {1 - (y - x[k])/(x[k + 1] - x[k]), x[k] <= y <= x[k + 1]}}];

Plot[Evaluate[aa[#][y] & /@ {0, 1, 2, 3}], {y, 0, 3}, PlotLegends -> "Expressions"]

Alternatively, you can plot each function aa[k][y] seperately and combine using Show:

Show[j = 1; 
 Plot[Evaluate[aa[#][y]], {y, 0, 3}, PlotStyle -> ColorData[3, "ColorList"][[k++]], 
    PlotLegends -> "Expressions"] & /@ {0, 1, 2, 3}]