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Okay, that's what I thought ....

It seems to me that in many cases it would be pretty clear, even with a not-very-high-resolution display, how many times are of f(x) = 0), and if it wasn't clear, you'd change the range over which the function's being graphed so that you get better resolution. It seems to me that it would be the same with doing the graph on paper -- *unless* part of doing the graph on paper was to determine analytically how many solutions there are. Which would be a good thing for people to practice, at some point.

Oh, you mean regular versus logarithmic .... I was thinking ranges (plotting a function for x = -10 to 10 versus plotting it for x = -1000 to 1000, say).

"Logarithmic paper", huh? I had forgotten that there was such a thing, but now that you mention it .... Well, maybe people do understand this better if they do the plots by hand rather than doing them with a gadget.

Depends on the tool, maybe? For the only one I'm really familiar with, the formulae would still be on the screen (in a different window), or they could be added to the plot as a -- I think the word I want is "legend"? the block of text to one side that says what each line in a multi-function plot represents?

Actually it seems to me that a gadget-tool that would let you easily "sketch" the effects of various transformations would be more helpful, at least in getting the basic ideas.

At some point it would also be useful to calculate the results of transformations -- maybe by hand, maybe using some calculator-like program you wrote yourself -- and graph the results. I don't get how doing the graphing by hand adds to the learning -- buttuming students have already had some practice with graphing functions.

And the only programming course(s) in which I can remember "parallel" or "concurrent" in the breastle. "How times change"? Maybe the people teaching CS1 courses figure they can't buttume that the students know enough linear algebra for buttignments like the ones you did to make sense. They probably *do* teach this in courses on graphics, or on scientific computing, but ....

-- B. L. Mbuttingill ObDisclaimer: I don't speak for my employers; they return the favor.