Operation Manual

Chapter 6: Sequence Graphing 113
Graphing Web Plots
Graphing a Web Plot
To select Web axes format, press y . ~ Í. A web plot graphs u(n) versus u(nN1), which you
can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence.
You can see how the sequence may change behavior as its initial value changes.
Valid Functions for Web Plots
When Web axes format is selected, a sequence will not graph properly or will generate an error.
• It must be recursive with only one recursion level (u(nN1) but not u(nN2)).
• It cannot reference
n directly.
• It cannot reference any defined sequence except itself.
Displaying the Graph Screen
In Web format, press s to display the graph screen. The TI-84 Plus C:
•Draws a
y=x reference line in AxesOn format.
• Plots the selected sequences with
u(nN1) as the independent variable.
Note: A potential convergence point occurs whenever a sequence intersects the
y=x reference line.
However, the sequence may or may not actually converge at that point, depending on the sequence’s
initial value.
Drawing the Web
To activate the trace cursor, press r. The screen displays the sequence and the current n, X, and Y
values (X represents u(nN1) and Y represents u(n)). Press ~ repeatedly to draw the web step by step,
starting at
nMin. In Web format, the trace cursor follows this course.
1. It starts on the x-axis at the initial value
u(nMin) (when PlotStart=1).
2. It moves vertically (up or down) to the sequence.
3. It moves horizontally to the
y=x reference line.
4. It repeats this vertical and horizontal movement as you continue to press ~.
Using Web Plots to Illustrate Convergence
Example: Convergence
1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to a default
í (Dot-Thick), and then define
nMin, u(n) and u(nMin) as u(n) = -.8u(n-1) + 3.6.