tc=ParametricPlot3D[{t,t^2,t^3},{t,-1,1},PlotStyle->{Yellow,Thick},BoxRatios->{1,1,1}]

p=ParametricPlot3D[{x,x^2,z},{x,-1,1},{z,-1,1},Mesh->None,BoxRatios->{1,1,1}];

Show[tc,p]

c=ParametricPlot3D[{x,y,x^3},{x,-1,1},{y,-1,1},Mesh->None,BoxRatios->{1,1,1}];

Show[tc,c]

f=y-x^2;
g=z-x^3;

r=ContourPlot3D[(x+y)f+(x^2-y z)g==0,{x,-1,1},{y,-1,1},{z,-1,1},Mesh->None,BoxRatios->{1,1,1}]

Show[r,tc]

Show[tc,p,c,r]

nr=ContourPlot3D[(x+y^2+z^5y^2-x^5)f+(x^2-y z)g==0,{x,-1,1},{y,-1,1},{z,-1,1},Mesh->None,BoxRatios->{1,1,1}]

Show[nr,tc]