when graph not correctly displayed and inequalities

[Sheila]

Recently, one of my students was graphing a cube root function and it
graphed as a square root function. I could not figure out what had
happened or what was the difference in settings on this handheld that
was causing it to happen. I opened new documents, turned off and on,
nothing changed. Finally I went to system settings and reset the
handheld to defaults and that corrected the problem. I was wondering
if anyone else has had this happen and if anyone knows what or why
this could have happened.

Second question: Does anyone know if ti is working on how the tinspire
graphs inequalities. Is there anything in the works that will allow
the tinspire to graph inequalities as a truth function like it can be
done on the 84?

[Nelson Sousa]

are you sure it _was_ a square root, or that it looked like a square root?

Given that once you reset the settings to factory defaults, my guess
is the following: the unit had the complex mode settings as
Rectangular or Polar; by reseting to the factory defaults, it gets
back to Real.

Now, why is this relevant?

1. x^(1/3) has only one real value; however, it can mean 3 different
complex numbers.

2. As computers don't like multivalued functions (nor do humans), we
have a convention where we take one of the cubic roots, the same way
as we take only the positive square root when we write x^(1/2).

3. With complex numbers set to Real, (-1)^(1/3) has only one real
solution, -1, so the negative part of the graph is plotted.

4. However, with complex numbers set to Rect or Polar, (-1)^(1/3) has
3 different solutions; two complex (pardon my language, they're all
complex; I mean 2 with non zero imaginary part) and one real solution.

And here lies the problem: what number does TI-Nspire return when we
ask for the result of (-1)^(1/3)? The answer is: the "first" one. As
all cubic roots have the same magnitude, TI-Nspire sorts them by
angle. So, the "first" solution has an angle of Pi/3, therefore the
result isn't real. So it's not plotted.

This is actually a MAJOR issue on graphing calculators (all of them,
actually, not only TI!). When plotting a calculator should always
assume that the only answers one's interested in are real answers, and
ignore all non-real ones. TI-Nspire is plotting the graphs the same
way as Voyage 200, TI-92 family and TI-89 family and take the first
complex solution, ordering them by angle.

The honorable exceptions to this rule are the TI-83 plus and TI-84
Plus families that ignore complex answers while in graphics,
regardless of mode settings.

In my view, a graphing calculator should always ignore complex
solutions when plotting graphs, regardless of mode settings. Graphs of
functions are always intended to be "graphs of real-value functions".
If one (in an engineering course, for example) want to plot a complex
valued function one is usually interested in plotting only the
magnitude, or plotting both the real part and imaginary part in
separate graphs, so this wouldn't be an issue for CAS.


As for inequations: I have no idea. I hope it's sometime soon, I have
a bunch of ideas waiting for inequations to be properly defined and
plotted...


Nelson

[Jaiwant and Joanne]

For inequalities... Use the backspace key on the input line in G&G.  Delete the = sign and replace with < or > or <= or >= and type in the function.  Press enter.... wow! Jay ---- --- On Sat, 28/3/09, Sheila <shor...@sbcglobal.net> wrote:

[Nelson Sousa]

yes, but they're just drawn, they're not defined. A lot of features
available for functions isn't available for inequalities. For
instance, recalling the function that defines the border on the
calculator app and use solve to determine the points of interest.

Nelson

[Sheila]

Wow!
thank you for your lengthy and detailed explanation. It was the cube
root function and it must have been in polar or rectangular mode. We
were graphing polar graphs in another class. I didn't understand what
was going on but now I have a better idea. I would expect a graphing
calculator to only graph the real values when in function mode but I
now have an explanation for my students. Thank you.
The inequalities are done so nicely on the 84 I did feel compelled to
show my students. It reallly is the first time that I felt the 84 did
a better job than the nspire.
Appreciate the quick response.
Sheila

> > done on the 84?- Hide quoted text -
>
> - Show quoted text -