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I am trying to graph the following surfaces so that they are all visible in the same place:

z == y^2 - y^3

on -3.5 < x < 3.5, -2 < y < 2, -3 < z < 3

 (x-3)^2 + y^2 == 0.25

on -3.5 < x < 3.5, -2 < y < 2, -3 < z < 0

(x+3)^2 + y^2 == 0.25

on -3.5 < x < 3.5, -2 < y < 2, -3 < z < 0

How can I graph these three functions on these different intervals?

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    $\begingroup$ Show[ContourPlot3D[ z == y^2 - y^3, {x, -3.5, 3.5}, {y, -2, 2}, {z, -3, 3}], ContourPlot3D[{(x - 3)^2 + y^2 == 0.25, (x + 3)^2 + y^2 == 0.25}, {x, -3.5, 3.5}, {y, -2, 2}, {z, -3, 0}]] $\endgroup$
    – cvgmt
    Commented Dec 9, 2023 at 1:41

1 Answer 1

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use Show as @cvgmt said

Show[ContourPlot3D[z == y^2 - y^3, {x, -3.5, 3.5}, {y, -2, 2}, {z, -3,
     3}], ContourPlot3D[(x - 3) ^ 2 + y^2 == 0.25, {x, -3.5, 3.5}, {y, -2,
     2}, {z, -3, 0}], ContourPlot3D[(x + 3) ^ 2 + y^2 == 0.25, {x, -3.5, 
    3.5}, {y, -2, 2}, {z, -3, 0}]]

enter image description here

and a variant.

Show[Plot3D[y^2 - y^3, {x, -3.5, 3.5}, {y, -2, 2}, PlotRange -> All],
     Graphics3D @ Cylinder[{{3, 0, -3}, {3, 0, 0}}, 0.5], Graphics3D @ Cylinder[
    {{-3, 0, -3}, {-3, 0, 0}}, 0.5]]

enter image description here

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