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In the UK we have similar questions of plotting and describing geometric functions, however we were simply taught how to plot them by hand, or just directly interrogate the equation to spot where an asymptote might be, roots etc.

IMO this gives a much better inherent understanding of equations, rather than just plugging in some numbers into a calculator and reading what comes out.

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Even I have two graphic calculators (HP not TI). I never used them really to draw even a single graph. I mostly use the larger display just to check and copy more easy previous results. On work I prefer these days to use just my HP35S (two lines display / RPN).

And yes, drawing the graph by yourself is for sure the way better way to learn something. But what do we know ...

I wasn't sufficiently clear above: use of graphing software isn't the only way the students are asked to investigate curves: they're taught the methods you're describing too. I presume the idea is to allow a much larger number of curves to be investigated in a given time which sort of makes sense given that the exercise is a form ML training.

Disclaimer: I'm originally from the UK and well versed in "old school" approaches :)

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