Toggle visibility of elements in a plot

Question

I have three simple graphs in one Plot. Now I am trying to make a button for each graph so you can hide or show it in the plot. Until now I was just able to make a checkbox with the Manipulate function, but I don't now how to tell the checkbox that it should hide my graph when unchecked an display it when checked.

Here is what I was able to make so far, I know it looks simple but I also have many other mathematica documents which at the end just need this button.

Answer 1

One way to do this is to use Opacity to hide a graph and empty label "" to hide a label:

Manipulate[
 Plot[{0.5 x + 1, x, 2 x - 2}, {x, -1, 5}, 
      PlotRange -> {-1, 5}, AspectRatio -> 1, 
      PlotStyle -> {Opacity[a], Opacity[b], Opacity[c]},
  Epilog -> {
    Text[If[a == 1, "f(x)", ""], {4.5, 2.7}],
    Text[If[b == 1, "y=x", ""], {4.5, 4}],
    Text[If[c == 1, "g(x)", ""], {3, 4.5}]
    }],
 {{a, 1, "f(x)"}, {1, 0}},
 {{b, 1, "y=x"}, {1, 0}},
 {{c, 1, "g(x)"}, {1, 0}}, ControlPlacement -> Left, 
 FrameMargins -> 0]

Answer 2

Manipulate is probably the easiest for this specific case but here is an alternative:

 DynamicModule[{select = {1, 2, 3}},

 Column[{
   CheckboxBar[
    Dynamic[select], {1 -> "g(x)", 2 -> "y=x", 
     3 -> "f(x)"}],
   Dynamic@Plot[Evaluate@{0.5 x + 1, 2 x - 2, x}[[select]], {x, -1, 5},
     PlotRange -> {-1, 5},
     AspectRatio -> 1,
     ImageSize -> 300,
     PlotStyle -> ColorData[1, "ColorList"][[select]]
     ]
   }]
 ]

DynamicModule[{select = {1, 2, 3}},

 Row[{
   CheckboxBar[
    Dynamic[select], {1 -> "g(x)", 2 -> "y=x", 3 -> "f(x)"}, 
    Appearance -> "Vertical"],
   Dynamic@Plot[Evaluate@{0.5 x + 1, 2 x - 2, x}[[select]], {x, -1, 5},
     PlotRange -> {-1, 5},
     AspectRatio -> 1,
     ImageSize -> 300,
     PlotStyle -> ColorData[1, "ColorList"][[select]]
     ]
   }]
 ]

Answer 3

As you mentioned that you wanted a GUI using Button

DynamicModule[{b = {True, True, True}, res, 
              funs = {0.5 x + 1, x, 2 x - 2}, pic},
              fun[val_] := If[val == True, "Pressed", "DialogBox"];
              res = Dynamic@
              Row@{Button["f(x)", If[b[[1]] == True, b[[1]] = False, b[[1]] = True],
                   BaseStyle -> {"GenericButton", 20, Bold}, Appearance->fun[b[[1]]]], 
                   Button["y(x)", If[b[[2]] == True, b[[2]] = False, b[[2]] = True],
                   BaseStyle -> {"GenericButton", 20, Bold},Appearance->fun[b[[2]]]], 
                   Button["g(x)", If[b[[3]] == True, b[[3]] = False, b[[3]] = True],
                   BaseStyle -> {"GenericButton", 20, Bold},Appearance->fun[b[[3]]]]
              };
              pic = Column[{res,Dynamic@Plot[
                     Evaluate@Flatten@MapThread[If[#1 == True, #2, Null] &,{b,funs}],
                     {x, -1, 5},PlotRange -> {-1, 5}, AspectRatio ->1,PlotStyle->Thick,
  Epilog -> {Text[If[b[[1]] == True, "f(x)", ""], {4.5, 2.7}], 
    Text[If[b[[2]] == True, "y=x", ""], {4.5, 4}], 
    Text[If[b[[3]] == True, "g(x)", ""], {3, 4.5}]},
  ImageSize -> 500]},
  Alignment -> Center, Frame -> True, Background -> {{LightRed, None}}
  ];
  pic
  ]