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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


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 
Associated Topics:
High School Calculators, Computers
High School Equations, Graphs, Translations
High School Functions

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