Implicit Plots - Texas Instruments TI-89 Manual Book

Implicit Plots

Explicit and Implicit
Forms
Tip: You can also graph
many implicit forms if you
either:
Express them as
parametric equations.
Refer to Chapter 7.
Break them into
separate, explicit
functions. Refer to the
preview example in
Chapter 6.
Selecting the Graph
Format Style
Note: From the Graph
screen, you can switch to
the other graph format
styles by pressing:
: Í
TI-89
F
TI-92 Plus:
However, to return to
press:
IMPLICIT PLOT
: ¥ Í
TI-89
: ¥ F
TI-92 Plus
An implicit plot is used primarily as a way to graph 2D implicit
forms that cannot be graphed in function graphing mode.
Technically, an implicit plot is a 3D contour plot with a single
contour drawn for z=0 only.
In 2D function graphing mode,
equations have an explicit form
y=f(x), where y is unique for
each value of x.
Many equations, however, have
an implicit form f(x,y)=g(x,y),
where you cannot explicitly
solve for y in terms of x or for x
in terms of y.
By using implicit plots in 3D graphing mode, you can graph these
implicit forms without solving for y or x.
Rearrange the implicit form as
an equation set to zero.
In the Y= Editor, enter the non-
zero side of the equation. This
is valid because an implicit plot
automatically sets the equation
equal to zero.
For example, given the ellipse
equation shown to the right,
enter the implicit form in the
Y= Editor.
In 3D graphing mode, define an appropriate equation and graph it as
you would any 3D equation, with the following exception. Display
the
GRAPH FORMATS
or Graph screen.
¥ Í
TI-89:
: ¥
TI-92 Plus F
Then set:
Style = IMPLICIT PLOT
y is not unique for each x, so
you cannot graph this in
function graphing mode.
f(x,y)ì g(x,y)=0
z1(x,y)=f(x,y)ì g(x,y)
If
then z1(x,y)=xñ +.5yñ ì 30.
dialog box from the Y= Editor, Window editor,
Chapter 10: 3D Graphing
xñ +.5yñ =30,
171