The function f:(ℝ^3)⟶ℝ, f(x,y,z)=(x^2)+(y^2)+(z^2)is composed with the curve c:ℝ⟶(ℝ^3)given by c(t)=(t,2t+2,0).  The composition (f∘c)(t)=(((t))^2)+(((2t+2))^2)+(((0))^2)=5(t^2)+8t+4 is a real-valued function on ℝ  But what does it mean?.

f[x_,y_,z_]:=x^2+y^2+z^2;levelsets=ContourPlot3D[{x^2+y^2+z^2},{x,-10,10},{y,-10,10},{z,-10,0},Mesh->None,ContourStyle->Opacity[.5],Contours->{0,1,5,10,20,40,60,85},PlotRange->{{-10,10},{-10,10},{-10,10}},Boxed->False,AxesOrigin->{0,0,0},ImageSize->400];
curve = ParametricPlot3D[{t,2t+2,0},{t,-20,20},PlotStyle->{Red,Thick}];
tdot[t_]:=Graphics3D[{PointSize[.02],Blue,Point[{t,2t+2,0}]}];
Manipulate[{Show[levelsets,curve,tdot[t]],":  the f-value along c"f[t,2t+2,0]},{t,-6,4}]