I'm not against using graphing programs in an educational setting, but I'm very concerned about limiting their use. I want students to know how to graph whatever it is they're supposed to graph, not just know how to use a computer or graphing calculator to generate a graph. As far as presenting material goes, I see that such programs have a valid place in the classroom.
It's one thing to say that all programs are not created equal, it's quite another to say that many don't graph correctly--but many don't! I have a "litmus test" function I use to determine if a program meets my minimum standards. If the program graphs it correctly, the program is probably good; if it doesn't graph it correctly, then I don't look any further.
What is the function, you ask? y=x^(2/3), or x to the two-thirds power. Some programs can't handle x being negative, others can't handle that the y-values are always non-negative. Additionally, the graph should be symmetric about the y-axis.
I know there are many such programs out there, most of them free, but one I've found recently, and one that's very easy to use, is the "Graph" program that can be downloaded here.
I think Macs come preloaded with a graphing program. If not, then please leave a comment about where you can download a Mac-based program that meets my litmus test above--same goes for pc-based programs. Have a favorite graphing program? Let us know!
10 comments:
Macintoshes come with a graphing program called "Grapher."
Sadly, it fails your test :-(
Nothing shows up for y<0.
-Mark Roulo
Macs come with an application called Grapher, which only graphs {x : x > 0}
Write the equation as y=(x^2)^(1/3)
It will now solve for x<0
Why would you need a graping program if you have Excel?
Grapher correctly plots y=(x^2)^(1/3) for all values of x. If you're looking to get a solution (the "incoming owl" graph), that's what you tell the program to plot. If you won't settle for having to translate your function from x^(2/3) to (x^2)^(1/3), then that's another story.
Microsoft Excel can't handle x^(2/3) for x<0, either. But it's perfectly happy to solve (x^2)^(1/3).
I prefer programs for which I do not have to find work-arounds for their shortcomings :-)
Sometimes you have to work with machines to get an answer. Speak to them in terms they understand.
Or you can wait for the machines to come to you while maintaining an attitude that it's the machine's shortcomings for not understanding you on your own terms.
I'm glad you're at least willing to type the function into the machine, observing the requisite formatting conventions (carats to identify exponents, asterisks to invoke multiplication, etc.).
Clearly, you never used a slide rule. Folks went through amazing contortions to coax answers from those devices.
You make my point for me. You had to go through "contortions" in order to accommodate the limitations of the slide rule. However, since that was the best tool available, people didn't complain too much.
Graph is a *free* program and is clearly superior to others through which you have to jump hoops in order to get a correct graph. Why do you fault me for wanting to use a superior program?
I own a slide rule.
"Sometimes you have to work with machines to get an answer. Speak to them in terms they understand.
Or you can wait for the machines to come to you while maintaining an attitude that it's the machine's shortcomings for not understanding you on your own terms."
Since this tool would be used by high school (?) math students, I wouldn't expect that they would necessarily:
(a) Know the correct answer (in this case that the function has solutions for y<0), and
(b) Know how to construct the workaround.
If the students "learn the wrong thing (e.g. Darren's function *can't* evaluate when y<0)" then this is *very* bad.
I, too, would hold out for a better tool if I was using it in an educational setting.
-Mark Roulo
I like the online graphing calculator, GCalc. You can graph multiple functions on the same screen, and it will draw them using different colors for each.
I frequently use it to create graphs when putting together worksheets for the students I tutor.
I've also found it useful to ask students to graph a parent function, tweak the equations and predict what will happen to the graph, and then check it against the graph of the original. GCalc makes this very easy.
(I tested your function with GCalc; you do have to input x^(2/3) as (x^2)^(1/3) if you want it to work for negative values of x.)
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