Decomposing A Rational Function - Texas Instruments TI-89 Manual Book

Decomposing a Rational Function

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.
394 Chapter 23: Activities
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.
To examine the decomposition of the rational function
f(x)=(xò ì 10xñ ì x+50)/(xì 2)
1. On the Home screen, enter the
rational function as shown
below and store it in a function
f(x) .
Enter: (
x^3ì 10x^2ì x+50)/
(xì 2)! f(x)
2. Use the proper fraction
function (
propFrac
function into a quotient and
remainder.
3. Copy the last answer to the
entry line.
—or—
Enter: 16/(xì 2)+x^2ì 8ù xì 17
4. Edit the last answer in the
entry line. Store the remainder
to and the quotient to
y1(x)
y2(x) as shown.
Enter:
16/(xì 2)! y1(x):
x^2ì 8ù xì 17! y2(x)
5. In the Y= Editor, select the
thick graphing style for
on a graph:
) to split the
.
y2(x)