mathematica Plot with Manipulate shows no output - wolfram-mathematica

Question

I was initially attempting visualize a 4 parameter function with Plot3D and Manipulate sliders (with two params controlled by sliders and the other vary in the "x-y" plane). However, I'm not getting any output when my non-plotted parameters are Manipulate controlled?
The following 1d plot example replicates what I'm seeing in the more complex plot attempt:
Clear[g, mu]
g[ x_] = (x Sin[mu])^2
Manipulate[ Plot[ g[x], {x, -10, 10}], {{mu, 1}, 0, 2 \[Pi]}]
Plot[ g[x] /. mu -> 1, {x, -10, 10}]
The Plot with a fixed value of mu has the expected parabolic output in the {0,70} automatically selected plotrange, whereas the Manipulate plot is blank in the {0, 1} range.
I was suspecting that the PlotRange wasn't selected with good defaults when the mu slider control was used, but adding in a PlotRange manually also shows no output:
Manipulate[ Plot[ g[x], {x, -10, 10}, PlotRange -> {0, 70}], {{mu, 1}, 0, 2 \[Pi]}]

Answer 1

This is because the Manipulate parameters are local.
The mu in Manipulate[ Plot[ g[x], {x, -10, 10}], {{mu, 1}, 0, 2 \[Pi]}] is different from the global mu you clear on the previous line.
I suggest using
g[x_, mu_] := (x Sin[mu])^2
Manipulate[Plot[g[x, mu], {x, -10, 10}], {{mu, 1}, 0, 2 \[Pi]}]
The following works too, but it keeps changing the value of a global variable, which may cause surprises later unless you pay attention, so I don't recommend it:
g[x_] := (x Sin[mu])^2
Manipulate[
mu = mu2;
Plot[g[x], {x, -10, 10}],
{{mu2, 1}, 0, 2 \[Pi]}
]
It may happen that you Clear[mu], but find that it gets a value the moment the Manipulate object is scrolled into view.

Answer 2

Another way to overcome Manipulate's localization is to bring the function inside the Manipulate[]:
Manipulate[Module[{x,g},
g[x_]=(x Sin[mu])^2;
Plot[g[x], {x, -10, 10}]], {{mu, 1}, 0, 2 \[Pi]}]
or even
Manipulate[Module[{x,g},
g=(x Sin[mu])^2;
Plot[g, {x, -10, 10}]], {{mu, 1}, 0, 2 \[Pi]}]
Both of which give
Module[{x,g},...] prevents unwanted side-effects from the global context. This enables a simple definition of g: I've had Manipulate[]ed plots with dozens of adjustable parameters, which can be cumbersome when passing all those parameters as arguments to the function.