f[x_] = Exp[-x^2] Sin[4  x]

g[x_] = 2 Exp[-x^2/3] Cos[6  x]

h[x_] := If[Abs[x] < 1, 1 - Abs[x], 0]

Plot[{f[x], g[x]}, {x, -5, 5}]

Plot[h[x], {x, -2, 2}]

Needs["Graphics`Animation`"]

Animate[
      Plot[f[z + t ]  +  g[z - t], {z, -10, 10}, 
        PlotRange -> {{-10, 10}, {-3, 3}}], {t, -10, 
        10}]

Animate[
      Plot[h[z + t ]  - 2  h[z - t], {z, -10, 10}, 
        PlotRange -> {{-10, 10}, {-3, 3}}], {t, -10, 
        10}]