Texas Instruments PLUS TI-89 - Manual (Page 164)

Chapter 9: Sequence Graphing 147
09SEQUEN.DOC TI-89/TI-92 Plus: Sequence Graphing (English) Susan Gullord Revised: 02/23/01 10:59 AM Printed: 02/23/01 2:14 PM Page 147 of 14
A sequence must meet the following criteria; otherwise, it will not be
graphed properly on
WEB axes. The sequence:
¦ Must be recursive with only one recursion level;
u(n ì 1) but not u(n ì 2) .
¦ Cannot reference n directly.
¦ Cannot reference any other defined sequence except itself.
After you select WEB axes and display the Graph screen, the
TI -89 / TI-92 Plus:
¦ Draws a y=x reference line.
¦ Plots the selected sequence definitions as functions, with u(n ì 1)
as the independent variable. This effectively converts a recursive
sequence into a nonrecursive form for graphing.
For example, consider the sequence u1(n) = 5ìu1(nì1) and an
initial value of ui1=1 . The TI -89 / TI-92 Plus draws the y=x reference
line and then plots y = 5 ì x .
After the sequence is plotted, the web may be displayed manually or
automatically, depending on how you set
Build Web on the AXES
dialog box.
If Build Web = The web is:
TRACE Not drawn until you press …. The web is then
drawn step-by-step as you move the trace cursor
(you must have an initial value before using
Trace ).
Note: With WEB axes, you cannot trace along the
sequence itself as you do in other graphing modes.
AUTO Drawn automatically. You can then press … to
trace the web and display its coordinates.
The web:
1. Starts on the x axis at the initial value ui (when plotstrt = 1 ).
2. Moves vertically (either up or down) to the sequence.
3. Moves horizontally to the y=x reference line.
4. Repeats this vertical and horizontal movement until n = nmax .
Using Web Plots
A web plot graphs u(n) vs. u(n ì 1), which lets you study the
long-term behavior of a recursive sequence. The examples in
this section also show how the initial value can affect a
sequence’s behavior.
Valid Functions for
Web Plots
When You Display
the Graph Screen
Drawing the Web
Note: The web starts at
plotstrt. The value of n is
incremented by 1 each time
the web moves to the
sequence (plotStep is
ignored).