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I want to plot 

Plot[{Exp[x],Sin[x]},{x,0,10}]

The issue is that Sin[x] and Exp[x] are not of the same order of magnitude, so we do not see Sin[x]. Therefore, I would like to set different y-axis but on the same graph. For Exp[x], the y axis would go from 0 to 25000 and for Sin[x] from -1 to 1. How can I do that ?

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    $\begingroup$ Why do you need to plot curves with widely-varying ranges together? $\endgroup$
    – J. M.'s slightly less busy ♦
    Oct 8, 2018 at 9:02
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    $\begingroup$ I have a case when I want to visualize the data and the log of the data. The curve is supposed to be an exponential at the beginning and vary linearly at the end. I want to see a linear evolution at the beginning with the log of the data, a linear evolution at the end with the data, and a transition area. I asked my question in a simple way, since the data is pretty big and that it's a general question $\endgroup$
    – J.A
    Oct 8, 2018 at 9:13
  • $\begingroup$ How about LogPlot? $\endgroup$
    – Αλέξανδρος Ζεγγ
    Oct 8, 2018 at 11:42
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    $\begingroup$ @ΑλέξανδροςΖεγγ: That won't work so well for a function that becomes negative, like Sin[x] does. (There are ways around this, of course.) $\endgroup$
    – Michael Seifert
    Oct 8, 2018 at 12:39
  • $\begingroup$ @MichaelSeifert Actually, it is about data rescaling. Admittedly, log function is not "good at" dealing with non-positive values, but it is not difficult to find a proper rescaling function to use. $\endgroup$
    – Αλέξανδρος Ζεγγ
    Oct 9, 2018 at 4:44

3 Answers 3

Reset to default
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Rescaling the y-coordinates:

rescaleShow[p1_, p2_] := Module[{g1, g2, pr1, pr2, rs1, rs2},
   {g1, g2} = Cases[{p1, p2}, _Graphics, Infinity];
   {pr1, pr2} = Last /@ PlotRange /@ {g1, g2};
   rs1 = With[{pr = Last@PlotRange[g1]}, Rescale[#, pr] &];
   rs2 = With[{pr = Last@PlotRange[g2]}, Rescale[#, pr] &];
   Show[
    p1 /. Line[p_] :> Line[Transpose@MapAt[rs1, Transpose@p, 2]],
    p2 /. Line[p_] :> Line[Transpose@MapAt[rs2, Transpose@p, 2]],
    PlotRange -> {0, 1}, Frame -> True,
    FrameTicks -> {{Charting`FindTicks[{0, 1}, pr1], 
       Charting`FindTicks[{0, 1}, pr2]}, {Automatic, Automatic}}
    ]
   ];

OP's example:

rescaleShow[
 Plot[Exp[x], {x, 0, 10},
  PlotStyle -> ColorData[97][1], PlotLegends -> {HoldForm@Exp[x]}, 
  Frame -> True, PlotRange -> All],
 Plot[Sin[x], {x, 0, 10},
  PlotStyle -> ColorData[97][2], PlotLegends -> {Sin[x]}]
 ]

Mathematica graphics

This method uses Plot so you get the Plot bells and whistles, like discontinuity processing, except for automatic coloring of the graphs: 

rescaleShow[
 Plot[Tan[x], {x, 0, 10},
  PlotStyle -> ColorData[97][1], PlotLegends -> {Tan[x]}, 
  Frame -> True],
 Plot[Sin[x], {x, 0, 10},
  PlotStyle -> ColorData[97][2], PlotLegends -> {Sin[x]}]
 ]

Mathematica graphics

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A slightly modified version using Overlay.

combine[data1_, data2_] := Overlay[{ListLinePlot[data1,
  Frame -> {True, True, False, False}, 
  FrameLabel -> {"x1", "y1"}, LabelStyle -> Directive[12, Blue], 
  PlotStyle -> Blue, PlotRange -> All, 
  ImagePadding -> {{50, 50}, {40, 40}}],
  ListLinePlot[data2, Frame -> {False, False, True, True}, 
  FrameTicks -> All, FrameLabel -> {{None, "y2"}, {None, "x2"}}, 
  LabelStyle -> Directive[12, Red], PlotStyle -> {Red, Dashed}, 
  PlotRange -> All, ImagePadding -> {{50, 50}, {40, 40}}]}, 
 Alignment -> Center]

data1 = Table[{x, Sin[x]}, {x, 0, 10, 0.01}];
data2 = Table[{x, Exp[x]}, {x, -5, 5, 0.01}];
combine[data1, data2]

enter image description here

One advantage here is that you can use any range for x and y.

You can use Plot as well in the combine and modify the appearance.

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  • $\begingroup$ +1 for the coding ingenuity, but honestly, for me this just reinforces the idea that a small multiple chart is often the way to go. $\endgroup$
    – Michael Seifert
    Oct 8, 2018 at 12:45
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Multiply, Sin[x] by, say, 1000 and rescale the right axis:

Plot[{Exp[x], 1000 Sin[x]}, {x, 0, 10}, Frame -> True, 
  FrameTicks -> {{Automatic, Charting`FindTicks[{-1000, 1000}, {-1, 1}]}, 
    {Automatic, Automatic}},
  PlotLegends -> {HoldForm @ Exp[x], Sin[x]}]

enter image description here

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2
  • $\begingroup$ Not to nitpick, but both curves use the left axis (according to the legend). $\endgroup$
    – Andreas Rejbrand
    Oct 8, 2018 at 18:26
  • $\begingroup$ thank you @AndreasRejbrand; good catch. Fixed now. $\endgroup$
    – kglr
    Oct 8, 2018 at 18:27

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