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Oh right. I was thinking of cases such as a parabola that either touches or crosses the x axis, and it would be hard to tell which with too large a range. You're right that there are other cases in which you'd want to increase the range rather than decreasing it.
Don't you have the same problem with a handmade graph on paper? Either way (calculator or paper) you have to choose a range, and you have to choose it right, but to do that it seems to me that you need analytical skills.
I don't get how this is different from what happens in a graphing calculator. Just as a quick spot check, I just tried using gnuplot to graph sin(x), without specifying a range, and I got a plot going from -10 to 10 that clearly shows the periodic behavior. You can't really tell from the plot that the interesting points are where x is a multiple of pi-2, but you wouldn't be able to tell that from a hand-made plot either, unless you knew it to start with.
Maybe it would be different with a graphing calculator, but differences among tools are probably not the point ....
It boils down to the math. Trade schools often do lots more advanced math than some liberal arts colleges. Math is seeping...
What short cuts are those? analytical skills to find solutions to f(x) = 0? as someone who frequently encounters students who don't seem to have retained much of whatever they learned about basic algebra 1, I guess I'm biased toward thinking of the analytical skills as more important.
1 Which might not be much -- a colleague with a background in math education says these days it's not taught very thoroughly in high school, which is -- dismaying at best, IMO. But that's a rant for another time, maybe.
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Somewhat tangential -- are there commonly-used ones other than regular and logarithmic (combined in whatever way -- i.e., log scale for both axes or just one)? I'm not thinking of any ....
Sure. I think anyone who's plotted exponential-order-of-growth functions (and knows about log scales) would recognize that.
What, that people don't know about regular versus logarithmic scale? Why? You could even do plots using a log scale without the special paper, which was what I was actually imagining doing before you mentioned the paper. We were probably a couple of posts into this thread before I really remembered that people doing graphs by hand would probably be using graph paper, which would help a lot in keeping things orderly.
This is the PCitis disease and has to do with new money, a.k.a. middle clbutt. Liberal-flavored types think that it is kind and laudable to protect the young from learning living lessons. What...
And teachers' unions are fighting this training tooth and nail in this state (Mbutt.). They appear to be winning...
Can you sum up the lesson? My impression is that many people (not you in particular or maybe at all) have some very strange ideas about what "infinity" means ....
It is sensible to increase emphasis in economics, history, advanced physics, biology etc after you have bootstrapped a country to wealth through mbutt production of engineers. But you cannot get away from the math...
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I think we'll have to agree to disagree here -- it seems to me that the real "buttociation between the math and its effects" learning happens in the process of producing the points to be plotted, not in plotting them.
replying to the rest in a follow-up to Brian Inglis's reply
-- B. L. Mbuttingill ObDisclaimer: I don't speak for my employers; they return the favor.
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