I wanna be able to use the Piecewise function such that I don't have to manually enter all the pieces. For example, say I define
f[x_]:={x,x^2,x^3}
Consider now
Plot[Piecewise[{{f[x][[1]],0<x<1},{f[x][[2]],1<x<2},{f[x][[3]],2<x<3}},{x,0,3}]
I want to be able to do this using some kind of loop inside Piecewise. How can I implement this