Piecewise Functions on TI Graphing Calculators

Date: 02/08/2005 at 22:06:50
From: Mark
Subject: graphing piecewise-define functions on the calculator

I was wondering if someone could tell me how to graph a piecewise-
defined function on a TI-83 plus graphing calculator?

None of the teachers in my high school know how to do it, and I have
absolutely no clue how to do this.

Date: 02/08/2005 at 23:08:36
From: Doctor Peterson
Subject: Re: graphing piecewise-define functions on the calculator

Hi, Mark.

I almost taught my class yesterday how to do this, but decided it 
wasn't worth the time it would take to explain it!  It's a little
tricky, and I was teaching some other tricky things already.

Assuming you have the same TI-83 manual I do, look on page 17-4 where
there is an example titled "Graphing Piecewise Functions".  They don't
really explain what they are doing, so I'll supplement it.

Let's take a simple case:

  f(x) = -x  if x < 0
         x^2 if x >= 0

Since there is no "if" operation (as there is, say, in Excel or in C)
for use within an expression, we use the fact that a logical
comparison has a "Boolean" value (true or false) which in the TI-83
means 1 or 0.  So the expression "x < 0" has the value 1 when x < 0 
and 0 when x >= 0.

Now, if we multiply -x by (x < 0), then when x < 0 we will get -x, and
when x >= 0 we will get 0.  We can do the opposite for the second 
piece of the function.  Our piecewise function, as entered in the
calculator, is then

  Y1=(-X)(X<0)+(X^2)(X>=0)

Both comparisons are entered using the Test menu.  For more pieces, 
the middle ones will use something like (X>5)(X<10) to express the
interval from 5 to 10.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/