Texas Instruments TI-89 - Decomposing a Rational Function

394 Chapter 23: Activities
23ACTS.DOC TI-89/TI-92 Plus: Activities (English) Susan Gullord Revised: 02/23/01 1:24 PM Printed: 02/23/01 2:20 PM Page 394 of 26
To examine the decomposition of the rational function
f(x)=(x
òì
10x
ñì
x+50)/(x
ì
2)
on a graph:
1. On the Home screen, enter the
rational function as shown
below and store it in a function
f(x)
.
Enter: (
x^3
ì
10x^2
ì
x+50)/
(x
ì
2)
!
f(x)
2. Use the proper fraction
function (
propFrac
) to split the
function into a quotient and
remainder.
3. Copy the last answer to the
entry line.
—or—
Enter:
16/(x
ì
2)+x^2
ì
8
ù
x
ì
17
4. Edit the last answer in the
entry line. Store the remainder
to
y1(x)
and the quotient to
y2(x)
as shown.
Enter:
16/(x
ì
2)
!
y1(x):
x^2
ì
8
ù
x
ì
17
!
y2(x)
5. In the Y= Editor, select the
thick graphing style for
y2(x)
.
Decomposing a Rational Function
This activity examines what happens when a rational function
is decomposed into a quotient and remainder. Detailed
information about the steps used in this example can be found
in Chapter 6: Basic Function Graphing and Chapter 3:
Symbolic Manipulation.
Decomposing a
Rational Function
Note: Actual entries are
displayed in reverse type in
the example screens.
Hint: Move the cursor into
the history area to highlight
the last answer. Press
¸
to copy it to the entry
line.