# Superimpose PlotLegends, Correctly

My aim is to plot each function with distinct style superimpose with color based upon parameter.

For instance, I have 3 functions of 1 variable and 1 parameter. Table command is used for iterating over parameter space & also for colouring the associated curve obtained from the Plot command. All 3 functions are plotted with 3 distinct plot style.

After scanning all...or may be I missed something in the search, but I'm not able to correct the PlotLegends misfit style both in Plot & ListPlot commands.

{k1, k2, dk} = {0.01, 0.09, 0.01};

f1[x_] = Sin[k x];
f2[x_] = Cos[k x];
f3[x_] = Sin[k x]*Cos[k x];

Plot[Evaluate[
Table[Style[{f1[x], f2[x], f3[x]},
ColorData["Rainbow"][(k - k1)/(k2 - k1)]], {k, k1, k2,
dk}]], {x, -5 Pi, 5 Pi},
PlotStyle -> {"", Dashing[0.03, 0.01], Dashing[0.004]},
PlotLegends -> {Placed[{"Amp1", "Amp2", "Amp3"}, {Right, Bottom}]}]


Improper syntax on dashing. Use this:

PlotStyle -> {"", Dashing[{0.03, 0.01}], Dashing[0.004]}


or better, to my taste

PlotStyle -> {Automatic, Dashing[{0.03, 0.01}], Dashing[0.004]}


e.g.

Plot[Evaluate[Table[Style[{f1[x], f2[x], f3[x]},
ColorData["Rainbow"][(k - k1)/(k2 - k1)]],
{k, k1, k2, dk}]], {x, -5 Pi, 5 Pi},
PlotStyle -> {Automatic, Dashing[{0.03, 0.01}],
Dashing[0.004]}, PlotLegends ->
{Placed[{"Amp1", "Amp2", "Amp3"}, {Right, Bottom}]}]


• I'm amending my default settings also to get the corrections you just suggested...but thanks for the relook. Commented Oct 15, 2023 at 9:08