[?] Plot function with two or more variables?

Questions
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1

Hey, guys! How are you?!
I’m taking Calculus 3 classes and I’m having difficulties with functions of two or more variables. Of course the app shows the 3D form, but in class we have to represent this functions in the plane… and obviously we can’t draw it with the same accurate of the app. So my question is: is there a way for Wolfram app to calculate the functions, plot the 3D graph, but also show the right way to graph in the plane?
Thank you very much!

2

Hi Mariana, doing just okay. Trouble with calculus class… I think I know exactly what you are talking about, but hopefully no one is bothering you about any Weierstrass functions. Here are a few different in-plane plots

g1 = ContourPlot[ Evaluate[x^4 + y^4 == Exp[#] & /@ Range[5]], {x, -5, 5}, {y, -5, 5}, PlotRange ->
{{-4, 4}, {-4, 4}}]
g2 = PolarPlot[ Evaluate[ r /. Solve[  Evaluate[
x^4 + y^4 /. {x -> r Cos[\[Theta]],   y -> r Sin[\[Theta]]}] == k, r][[1]] /. k -> Exp[#] & /@
Range[5]], {\[Theta], 0, 2 Pi},   PlotRange -> {{-4, 4}, {-4, 4}}];
g3 = DensityPlot[x^4 + y^4, {x, -5, 5}, {y, -5, 5}];
g4 = ArrayPlot@ Table[ArcTan[x^4 + y^4], {x, -5, 5, .01}, {y, -5, 5, .01}];

GraphicsGrid[{{ g1, g2 }, { g3 , g4 }}]

PlanePlots.png
PlanePlots.png360×360 24.1 KB

If you really look into it, everything in-plane can be drawn with Graphics:

Head /@ {g1, g2, g3, g4}
Out[]=  {Graphics, Graphics, Graphics, Graphics}

I think direct use of the Graphics function is the way to get highest quality results. Read The Function Manual!