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I have a function of two variables

f[x_,t_]:= ...

and I want to build a command that plots the list of functions {f[x,t_i]} given any list of parameter values {t_i}. For example, I'd like

MyPlottingCommand[{1,2,3}]

to effectively execute the command

Plot[{f[x,1],f[x,2],f[x,3]},{x,0,10}]

I'd also like to add a plot legend that labels each function as "t = (value)" where (value) is t_i. This seems simple enough but I'm not so familiar with manipulating lists in Mathematica. Any advice is appreciated.

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1 Answer 1

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Clear[x]
f[x_, t_] := x + t
ts = Range[3]
exprs = f[x, #] & /@ ts
lbls = StringTemplate["t=``"] /@ ts
Plot[Evaluate@exprs, {x, 0, 10}, PlotLegends -> lbls]
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  • $\begingroup$ Actually this is giving me some trouble when I try to use it on my real example. The problem (I think) is that my function f has NIntegrate commands, which it is trying to evaluate at the line exprs = f[x,#]&/@ts. It can't evaluate these without actual values for x, so it throws errors. $\endgroup$
    – WillG
    Nov 7, 2019 at 19:11
  • $\begingroup$ Is there a way I can use something like f[x,#]/@ts without having MM actually try to evaluate f at this point? I just want it to automatically generate the list with other variables as placeholders so that it can be safely plugged into Plot. $\endgroup$
    – WillG
    Nov 7, 2019 at 19:13
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    $\begingroup$ @WillG You might want to try f[x_?NumericQ, t_?NumericQ] := .... This should prevent MMA from evaluating f[x, t] until it has actual numbers that it can use. $\endgroup$
    – MassDefect
    Nov 7, 2019 at 19:18
  • $\begingroup$ Thanks, that did the trick. $\endgroup$
    – WillG
    Nov 7, 2019 at 20:50
  • $\begingroup$ For posterity, I also had to throw in an "Evaluate[ ]" around the first argument of Plot when I wrote out "exprs" explicitly in that slot. I.e., "Plot[f[x,#]&/@ts,...]" and "Plot[Evaluate@f[x,#]&/@ts,...]" did not work, but "Plot[Evaluate[f[x,#]&/@ts],...]" did work. $\endgroup$
    – WillG
    Nov 7, 2019 at 20:53

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