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You're right, your way of doing it does show a lot more features. The problem I was solving included a constant R term as a value of r, and since I can't plot a function with an undefined constant, I just set R=1. Since the function in the problem...
Thanks Simon, I didn't know that it was possible to write a loop like that.  I've seen my textbook's plots of functions who's amplitudes are made up of undefined constants; the textbook then shows a plot who's vertical axis' units are multiples of...