daszek1[x_,t_]:=Piecewise[{{0,(x≤t)||(x≥t+2)},{x-t,(x≥t)&&(x≤t+1)},{-x+t+2,(x≥t+1)&&(x≤t+2)}}]
daszek2[x_,t_]:=Piecewise[{{0,(x≤-t)||(x≥-t+2)},{x+t,(x≥-t)&&(x≤-t+1)},{-x-t+2,(x≥-t+1)&&(x≤-t+2)}}]
u[x_,t_]:=((daszek1[x,t]+daszek2[x,t])/2)

Animate[Plot[daszek1[x,t],{x,-6,6},PlotRange->{0,1}],{t,0,2}]
Animate[Plot[daszek2[x,t],{x,-6,6},PlotRange->{0,1}],{t,0,2}]
Animate[Plot[u[x,t],{x,-6,6},PlotRange->{0,1}],{t,0,2}]