How do you put a plot inside a popupmenu that is inside another popupmenu?

Question

I have the next code

 Manipulate[
     Switch[x, a, If[selection =!= None, selection = None], b, 
        If[selection === None, selection = None], c, 
        If[selection === None, selection = "Hola"]
 ];
 selection, {x, {a, b, c}, ControlType -> PopupMenu},  
 {{selection, None}, 
     Switch[x, a, {"recta", "parabola"}, b, {"hiperbola", "absoluto"}, 
     c, {"Seno", "Coseno"}], ControlType -> PopupMenu}
 ]

but I need you to choose the second popupmenu I plot the function chosen.

Answer 1

Actually, I have to admit I do not quite understand what you are aiming for, so here's a long shot...

I understand that you want to have values in the second control (selection) that do depend on the first control, x that is.

Also, based on the title, I added some plots in the PopupMenu. Looks fun.

I hope it helps in some way. The key issue is that I introduced a helper, called selChoice to keep track of the updated selection-list. selChoice has ControlType None, so you won't see it in the actual Manipulate.

a = "Algebraicas";
b = "Trigonometricas";
c = "Tercer Grado";

Module[{myPlot},
    myPlot[f_] := Plot[f[x], {x, -5, 5}];
    Manipulate[
       Switch[x,
          a, If[selection =!= None, selection = None],
          b, If[selection === None, selection = None],
          c, If[selection === None, selection = "Hola"]];
       selection,
       {x, {a, b, c}, ControlType -> PopupMenu}, 
       {{selection, None}, selChoice, ControlType -> SetterBar},
       {{selChoice,
           Which[x == a, myPlot /@ {# &, #^2 &},
              x == b, myPlot /@ {#^3 &, Abs@# &},
              x == c, myPlot /@ {Sin, Cos}]}, None}]]

Note that I have no clue what you want to do with the first Switch... and also note that I am fully aware that my functions do not quite make sense in the respective categories.

Output:

EDIT

Based on the comment, maybe this is more what you want (I am still not sure)

Module[{myPlot}, myPlot[f_] := Plot[f[x], {x, -5, 5}];
  Manipulate[
    myPlot@selection, 
      {x, {a, b, c}, ControlType -> PopupMenu}, 
      {{selection, None}, selChoice, ControlType -> SetterBar}, 
      {{selChoice, Which[
         x == a, {# &, #^2 &}, 
         x == b, {#^3 &, Abs@# &}, 
         x == c, {Sin, Cos}]}, None}]]