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 Discussion: All Topics Topic: How to disconnect a piecewise graph

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 Subject: RE: How to disconnect a piecewise graph Author: Jonah Date: Mar 4 2007
On Feb  3 2007, MGB wrote:
> On Jan 30 2007, Betty14 wrote:
> If given a piecewise function,
> f(x)={x^2 for x<0; 2 for 0<=x<=2; x-1
> for x>2. How should I
> format the graph calculator (TI-83/83+/84+) in
> order to obtain a
> disconnected graph instead of getting a connecting
> graph
> throughout the domain of the function?

Hello, you can trick your
> calculator into doing the piecewise function by doing the following:
> y1=(x^2)/(x<0)
y2=(2)/((x>=0)and(x<=2))
y3=(x-1)/(x>2)

note:
> You can get the inequality symbols from the  2nd TEST menu (on the
> MATH) button and the "and"  from the TEST and then LOGIC.

How
> does it work? The 83/84 thinks of a true statement as a 1 and false
> as 0.  When the calculator is trying to graph y1, numbers less than
> 0 are true so the calculator divides by 1 and gets displayed, for
> numbers greater than 0 it divides by 0 and doesn't graph values that
> are undefined.

Look at the TABLE to see what is going on.
Good
> Luck.

I never considered this as an option on the graphing calculator.  Now my
students can get more exposure to different types of piecewise functions
quickly.

This year I taught it by hand and used the individuals graphs for reference and
tried to explain that it the particular graph would only be true given the
stipulations such as x<0.  I also had then find the values at the enpoints of
each domain to find the endpoints whether an actual point on the function or an
open dot representing the end of the function.  Still I had many struggles with
teaching this concept in Pre-Calculus this year.

I think graphing the piecewise functions on the TIs is a great visual that I can
add to my instruction next year.  Are there any other tools or advice when
teacing piecewise functions?