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I am currently learning the basics of Mathematica. I can't seem to find a straightforward answer in the Wolfram documentation, probably for a lack of clarity in my queries.

For example, I want to plot $f=\frac{a}{x}$ with $x=\frac{y}{b}$, and manipulate the variable $y$, but obtain a graph with $x$ on the $x$-axis.

On Mathematica I would write:

f=a/x;
x=y/b;
Plot[f,{y,0,10}]

This gives me the correct resulting plot but, of course, with the ticks'values of $y$ on the $x$-axis, instead of the ones of the dependent variable $x$. Do I need to change the ticks, or is there a more elegant way to achieve a plot with the values of $x$ on the $x$-axis?

Thank you.

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  • 4
    $\begingroup$ Try with ParametricPlot reference.wolfram.com/language/ref/ParametricPlot.html $\endgroup$ – mattiav27 Sep 24 '18 at 18:30
  • $\begingroup$ I am not sure I understand this. You want x on the x axis and a/x on the y axis? Where does y and b come into this? $\endgroup$ – Hugh Sep 24 '18 at 18:52
  • $\begingroup$ @mattiav27 thank you! That's exactly what I was looking for. $\endgroup$ – bg_da Sep 24 '18 at 18:59
  • $\begingroup$ @Hugh Yes, x on the x-axis, and a/x on the y-axis. y is the only variable by which x depends on, as the values of a and b are known. What I needed was the ParametricPlot command. $\endgroup$ – bg_da Sep 24 '18 at 19:04
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A static solution can be written like this:

With[{a = 1., b = .4, tmin = 0, tmax = 10},
  Block[{f, x, xticks},
    f[u_] := a/u;
    x[u_] := u/b; 
    xticks = {#, Round[x[#], .1]} & /@ Subdivide[tmin, tmax, 11];
    Plot[f[x[t]], {t, tmin, tmax},
      PlotRange -> {Automatic, {0, 3}},
      Ticks -> {xticks, Automatic}]]]

plot

A more interesting dynamic solution looks like this:

With[{tmin = 0, tmax = 10},
  Manipulate[
    Dynamic @
      Plot[f[x[t]], {t, tmin, tmax},
        PlotRange -> {Automatic, {0, 3}},
        Ticks -> {xticks, Automatic}],
    {{a, 1.}, 0, 2, .1, Appearance -> "Labeled"},
    {{b, 1.}, .1, 2, .1, Appearance -> "Labeled"},
    {xticks, None},
    Initialization :> (
      f[u_] := a/u;
      x[u_] := u/b; 
      xticks := {#, Round[x[#], .1]} & /@ Subdivide[tmin, tmax, 11])]]

demo

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