Domain of a function

[kley2011]

How do you determine the domain of a function using Ti-Nspire Cas with
touchpad? Is there a program for this or in what menu should I go to
look it up?

thank you very much

[John Hanna]

Re: How do you determine the domain of a function using Ti-Nspire Cas with

touchpad? Is there a program for this or in what menu should I go to
look it up?

You could look at the graph.
John Hanna
jeh...@optonline.net
www.johnhanna.us
T3 - Teachers Teaching with Technology
"A cowchip is paradise to a fly."

thank you very much

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[kley2011]

I am pretty new to this. I could look at the graph all day and see
nothing but what do I look at the graph and how I find this domain?

On Feb 12, 10:57 am, John Hanna <johneha...@gmail.com> wrote:
> Re: How do you determine the domain of a function using Ti-Nspire Cas with
> touchpad? Is there a program for this or in what menu should I go to
> look it up?
>
> You could look at the graph.
> John Hanna

> jeha...@optonline.netwww.johnhanna.us

> T3 - Teachers Teaching with Technology
> "A cowchip is paradise to a fly."
>
> -----Original Message-----
> From: tins...@googlegroups.com [mailto:tins...@googlegroups.com] On Behalf
>
> Of kley2011
> Sent: Saturday, February 12, 2011 9:57 AM
> To: tinspire
> Subject: [tinspire] Domain of a function
>
> How do you determine the domain of a function using Ti-Nspire Cas with
> touchpad? Is there a program for this or in what menu should I go to
> look it up?
>
> thank you very much
>
> --
> To post to this group, send email to tins...@googlegroups.com
> To unsubscribe send email to tinspire+u...@googlegroups.com

> For more options, visit this group athttp://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB

[Nelson Sousa]

What John is trying to tell you is that if you look at the graph and
spot a point where the function goes to infinity at a given point it
gives you a clue that that point is not in the function's domain.

However:
- not all points will be visible in the graph; just take 1(x-1000000);
the point x=1000000 is not in the function's domain and you won't see
it in the graph unless you adjust the window settings;
- you won't find "holes" in the function by simple inspection of the
graph: (x-3)^2/(x-3) has a hole at x=3 but it won't be visible in the
graph.

The only way to determine a function's domain is by inspection of its
expression; split it into elementary functions, determine their
domains and get the domain of the whole function by applying the chain
rule. There's no foolproof automatic answer.

Nelson

[Ray Fox]

AND use logic. While (x^2 -)/(x-1) looks like the domain is all real numbers, you have to take into consideration x cannot = 1 (cannot divide by 0).

Just looking at the graph will not show a hole without special handling.

[alcoonslists]

As Ray implies, even if the calculator/computer graph could show the domain of a function (inputs for which the function is defined) well by showing asymptotes and holes, there is not guarantee that your window(s) would be correct to show them.  In fact, our precalculus course course spends a good deal of time and energy to identifying domains of complicated functions (such as the compositions of two functions, e.g,  f(x)=ln(sin x)).  

All who use mathematical graphers need to have a good understanding of the limits of their technology.  They also need to limit the domains of functions so they work appropriately to model the phenomena they are to represent.  Hopefully this will also spill over when students move into other imaging fields.  For example, they need to worry about the artifacts produced by the software/hardware.

Not sure I was responding directly to the question-at-hand now that I think about it, but felt like throwing the last part in :)

Al

-------------------------

Albert Coons

al_c...@bbns.org

Buckingham Browne & Nichols School

Gerry's Landing Road

Cambridge, MA 02138

(617) 800-2264

AP Statistics Web Site:  www.bbn-school.org/us/math/ap_stats

[kley2011]

Thank you very much everyone. It looks like I am going to have to get
my calc and start practicing hard on this one.

On Feb 12, 4:24 pm, alcoonslists <alcoonsli...@verizon.net> wrote:
> As Ray implies, even if the calculator/computer graph could show the domain of a function (inputs for which the function is defined) well by showing asymptotes and holes, there is not guarantee that your window(s) would be correct to show them.  In fact, our precalculus course course spends a good deal of time and energy to identifying domains of complicated functions (such as the compositions of two functions, e.g,  f(x)=ln(sin x)).  
>
> All who use mathematical graphers need to have a good understanding of the limits of their technology.  They also need to limit the domains of functions so they work appropriately to model the phenomena they are to represent.  Hopefully this will also spill over when students move into other imaging fields.  For example, they need to worry about the artifacts produced by the software/hardware.
>
> Not sure I was responding directly to the question-at-hand now that I think about it, but felt like throwing the last part in :)
>
> Al
> -------------------------
> Albert Coons

> al_co...@bbns.org

> Buckingham Browne & Nichols School
> Gerry's Landing Road
> Cambridge, MA 02138
> (617) 800-2264
>
> AP Statistics Web Site:  www.bbn-school.org/us/math/ap_stats
>
> On Feb 12, 2011, at 2:53 PM, Ray Fox wrote:
>
> > AND use logic. While (x^2 -)/(x-1) looks like the domain is all real numbers, you have to take into consideration x cannot = 1 (cannot divide by 0).
> > Just looking at the graph will not show a hole without special handling.
>

> > On Sat, Feb 12, 2011 at 9:57 AM, John Hanna <johneha...@gmail.com> wrote:
> > Re: How do you determine the domain of a function using Ti-Nspire Cas with
> > touchpad? Is there a program for this or in what menu should I go to
> > look it up?
>
> > You could look at the graph.
> > John Hanna

> > jeha...@optonline.net

[jwilson828]

There are two great activities on the Math Nspired site for Domain and
Range. Go to education.ti.com > Downloads & Activities > Math Nspired.
Domain and Range is in the Functions and Relations unit for Algebra 1.
Domain and Range 2 is in the Functions unit for Algebra 2.

They certainly don't address all of the issues that come up with
domain and range, but they can give you a good background for
understanding domain and range.

Jennifer Wilson

[Travis Bower]

See if you can go directly...

Alg 1

http://education.ti.com/calculators/timathnspired/US/Activities/?t=5034&sa=5022

Alg 2

http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=1010&t=1163&id=16012

[Joe]

Kley, I'd like to take a different approach to answering your
question. Surely the TI Cas can be programed to determine the domain
of a function but just as surely, there are some things in math that
should not require the use of a calculator and I think that
determining the domain of a function is probably one of them. Just
assume that the permissible values for the independent variable are
all real numbers from minus infinity to plus infinity but then
eliminate any values that would cause a zero denominator because we
don't do division by zero, and eliminate values that would result in
the square root of a negative number, and what you are left with is
called the domain. For example the domain of y or f(x)=x^2+5 is all x
from minus infinity to plus infinity, but the domain of y or f(x)=1/
(x-1) has to leave out x=1 because that would represent division by
zero, and for f(x)=sqrt(x+1), where sqrt=square root, x+1 cannot be
negative, that is we must have x+1=>0 which means that x=>-1 and that
would be the domain. Hope that helps.

[Glenn]

Guys,

I have a function that I upgraded from my voyage functions that gives
the values of x (or any specified var) where the expr is undefined.

It's named realdm.

You can download a copy of it from:

http://gefisher.comxa.com/TI-Nspire/MyLib/

I plan to update it so that it accepts a string expr so that it can do
things like (x^2-1)/(x-1).

Let me know what you think of it. It will do u\realdm(ln(sin(x)),x).

Glenn.

[deobra]

This is an excellent explanation of domain in simplest terms for
someone who hasn't done these basics for a long time.
Debbie

[Joe]

Tthank you.

> > > thank you very much- Hide quoted text -
>
> - Show quoted text -

[Glenn]

All,

I made a mistake here. It should be:
Let me know what you think of it. It will do al
\realdm(ln(sin(x)),x).

It's in the al.tns.

Read the text file "ReadMe" for a description of the current files.

sorry,

Glenn.
--
Glenn E. Fisher University of Houston - Retired
Glenn E Fisher
gefi...@me.com
http://gefisher.comxa.com/gindex.html

Pure mathematics is, in its way, the poetry of logical ideas. --Albert
Einstein

On Feb 13, 8:56 pm, Glenn <gefis...@mac.com> wrote:
> Guys,
>
<snip>

> It's named realdm.
>
> You can download a copy of it from:
>
> http://gefisher.comxa.com/TI-Nspire/MyLib/
>
> I plan to update it so that it accepts a string expr so that it can do
> things like (x^2-1)/(x-1).
>
> Let me know what you think of it.  It will do u\realdm(ln(sin(x)),x).
>
> Glenn.
>
> On Feb 13, 4:47 pm, Joe <wjb...@yahoo.com> wrote:
>

<snip>

[kley2011]

Thank you guys. You are awesome. Glenn, I went to your website but it
looks like your file is no longer for download. Thanks for the effort!

On Feb 15, 8:53 am, Glenn <gefis...@mac.com> wrote:
> All,
>
> I made a mistake here.  It should be:
>  Let me know what you think of it.  It will do al
> \realdm(ln(sin(x)),x).
>
> It's in the al.tns.
>
> Read the text file "ReadMe" for a description of the current files.
>
> sorry,
>
> Glenn.
> --
> Glenn E. Fisher University of Houston - Retired
> Glenn E Fisher

> gefis...@me.comhttp://gefisher.comxa.com/gindex.html