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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) =
5
ì
u1(n
ì
1) 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).