# Plotting Several Functions w.r.t. Sqrt[variable]

I have the following plots in Mathematica but I would like to plot them with respect to Sqrt[s] instead of s. How would I do that?

p1 = Plot[{Abs[
Subscript[f, 1][s]/(s - (Subscript[σ, 1][s])^2)]/191.36,
Abs[Subscript[f, 5][s]/(s - (Subscript[σ, 5][s])^2)]/38,
Abs[Subscript[f, 50][s]/(s - (Subscript[σ, 50][s])^2)]/4,
Abs[Subscript[f, 100][s]/(s - (Subscript[σ, 100][s])^2)]/
2.48878}, {s, 3.5, 5.0}, PlotLegends -> {"0.1", "0.5", "5", "10"},
PlotLabel ->
"\!$$\*SubscriptBox[\(P$$, $$1$$]\) amplitudes: M=2.1, \
\!$$\*SubscriptBox[\(m$$, $$1$$]\)=\!$$\*SubscriptBox[\(m$$, \
$$2$$]\)=1", PlotRange -> All,
AxesLabel -> {"E", "|\!$$\*SubscriptBox[\(P$$, $$1$$]\)|"},
ImageSize -> Large]

• It is good practice to present a minimal example, rather than just cutting and pasting the code you are working on. You are more likely to get a helpful response if you do. – mikado Aug 10 at 20:22
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You can use ScalingFunctions (although sometimes it messes up the ticks):

Plot[Sin[Pi s], {s, 1, 8}, PlotRange -> All,
ScalingFunctions -> {{Sqrt, #^2 &}, Automatic}]


The ticks seem to be log-scale choices. Here's a way around that if desired:

Plot[Sin[Pi s], {s, 0, 8}, PlotRange -> All,
ScalingFunctions -> {{Sqrt, #^2 &}, Automatic},
Ticks -> {ChartingScaledTicks["Linear", {Sqrt, #^2 &}, "Nice"], Automatic}]


You can use Block to effect a change of plot variable e.g.

Block[{s = sqrts^2},
Plot[Sinc[Pi s], {sqrts, -5, 5}, PlotRange -> All]]
`