This came up in response to a student’s question.
I wrote that, in general, you can plot a function y(x) on a simple graph. You can plot y(x,x2) by plotting y vs x and then having several lines showing different values of x2 (for example, x2=0, x2=0.5, x2=1, x2=1.5, x2=2, etc). You can plot y(x,x2,x3,x4) by making a two-dimensional grid of plots, where the rows show different values of x3 and the columns show different values of x4.
Then I thought I should illustrate with a graph:
It took me about an hour to make this in R (or maybe half an hour, as I was doing other things at the same time). The code is really ugly; see below. Among other things, I had difficulty with the expression() function in R. I expect it should be much easier and more effective to do this in ggplot2.
Anyway, below is my code, which I include not out of pride but out of honesty. I could clean it up a bit but I might as well show you what I did. In any case, the grid of graphs illustrates the general point of how to plot a function of many variables, a point which I don’t think is as well known as it should be.