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This question already has an answer here:

How to colour the region "under" the curve? Given that $0<x<3$, $-4<y<4$, $0<z<4$

ParametricPlot3D[{3/2, y, Abs[y]/(3/2)^(1/4)}, {y, -4, 4}]

enter image description here

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marked as duplicate by Alexey Popkov, MarcoB, Feyre, corey979, m_goldberg plotting Jan 22 '17 at 0:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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You can use ListPointPlot3D

ListPointPlot3D[
 Table[{3/2, y, Abs[y]/(3/2)^(1/4)}, {y, -4, 4, 0.001}], 
 ColorFunction -> "BlueGreenYellow", Filling -> Bottom]

enter image description here

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