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Here is another solution that uses Checkboxes to display function choices as suggested by David R and David P, and ensures the viewing window and axes remain unchanged (specifying an explicit PlotRange is still a good idea). Note that a PlotStyle for...
Change the first argument of Plot from f[x] to Evaluate[f[x]].
First define the function f. The Basic Math Assistant palette has a button to "Define function" (open the palette from the Palettes menu and click on the Advanced tab of the palette in the Calculator section) that inserts a template for defining...