f[x_]=Piecewise[{{1-x^2,-1<x<1}},0]
Plot[f[x],{x,-5,5},PlotRange->{-1,1}]

g[x_]=Piecewise[{{Sin[3*x]+Cos[5*x],-1<x<1}},0]
Plot[g[x],{x,-5,5},PlotRange->{-2,2}]

Manipulate[Plot[f[x-c*t]+g[x+c*t],{x,-5,5},PlotRange->{-2,2}],{t,-2,2},{c,1,5}]