Scale in plot and Piecewise

Question

I wrote this code:

ClearAll[t]
 n = 4;
t[0] = 0;
t[n] = 1;
h = N[(t[n] - t[0])/n, 2];
Do[t[L + 1] = t[L] + h;, {L, 0, n - 1}]
 A[0][t_] := 
 Piecewise[{{1 - (t - t[0])/(t[1] - t[0]), t[0] <= t <= t[1]}}] 
A[k_][t_] := 
  Piecewise[{{(t - t[k - 1])/(t[k] - t[k - 1]), 
     t[k - 1] <= t <= t[k]}, {1 - (t - t[k])/(t[k + 1] - t[k]), 
     t[k] <= t <= t[k + 1]}}];
A[n][t_] := 
  Piecewise[{{(t - t[n - 1])/(t[n] - t[n - 1]), 
     t[n - 1] <= t <= t[n]}}];
Plot[Evaluate[A[#][t] & /@ Range[0, n]], {t, 0, 1}, 
 PlotRange -> {0, 1}, PlotLegends -> "Expressions"]

I want to have scale in distance for Piecewise, for example in the following picture

Answer 1

• Changed h = N[(t[n] - t[0])/n, 2]; to h = (t[n] - t[0])/n;
• Changed Piecewise[...] to Simplify@Piecewise[...], and
• Used t /@ Range[0, n] as horizontal axis ticks:

With these changes:

 Plot[Evaluate[A[#][t] & /@ Range[0, n]], {t, 0, 1}, 
     PlotRange -> {0, 1}, PlotLegends -> "Expressions", 
     Ticks -> {t /@ Range[0, n], Automatic}]

Use Ticks -> {{#, N[#, 2]} & /@ t /@ Range[0, n], Automatic} if you want tick labels as decimal numbers.

Without the change in the definition of h we get:

Answer 2

Have a look at AxesOrigin and FindDivisions

Plot[Evaluate[A[#][t] & /@ Range[0, n]]
, {t, 0, 1}
, PlotRange -> {{-.25, 1.22}, {-.25, 1.25}}
, AxesOrigin -> {-.25, -.25}
, Ticks -> {FindDivisions[{0, 1}, 4], Automatic}
, PlotLegends -> "Expressions"]