Geometry Explorer Help
Using the Graph Menu:
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Using Geometry Explorer one can graph the
relationship between two measured
quantities. The menu titled "Graph" has four groups of options
which control
graphing: Axes and Grid lines, Defining Functions, Adding
Points to Graphs, and Miscellaneous Options.
Axes and Grid Lines:
(Show/Hide) Axes:
Coordinate axes are always available
in Euclidean Geometry. However, the axes are hidden
initially. To see the axes use this menu option. Once the axes are
visible,
the menu item will change to "Hide Axes", allowing one to make the axes
invisible.
Grid (On/Off):
Grid lines are hidden
initially. To see the grid lines use this menu option. Once the grid
lines are visible,
the menu item will change to "Grid Off", allowing one to make the grid
lines
invisible.
Here is an example with
axes and grid lines both visible. Note that tic marks are shown on the
axes to help identify coordinate
values. Slightly longer tic marks denote multiples of the unit length
(2,3,4,etc.). Also, note that an axes system is composed of two
perpendicular lines, a point that serves as the origin, and a point on
the positive x-axis that serves as the unit point, i.e. the point at
(1,0) in this coordinate system.

Defining
Functions:
Add Function to
Graph...: Use this option to add a function to the coordinate
system. Once the option is chosen, a dialog box will open up as
shown. You have the option of defining a standard y=f(x)
function, a polar function (r = f(theta)), or a parametric function (h
= (x(t), y(t)). To input a function, type the name, the
expression defining the function, and the minimum and maximum values
for x (or theta or t, depending on the type of function), and hit Okay.
Here is what will be
plotted in the main window:
If we want to input a
parametric function, we type it in using parentheses as shown in the
dialog box below. Note that we can type in "pi" and the system will
understand what we mean.
Here is what will be
plotted in the main window:
Adding
Points to Graphs:
Add As (x,y): We
can add coordinate pairs to the coordinate system by selecting
(in order) 1) the measurement that will serve as the x-coordinate and
2)
the measurement that will serve as the y-coordinate. In the
figure
below we have created a circle and now we want to graph the
relationship
between the radius of the circle and its area. We select the
radius distance (for x), then the area measurement (for y).

At this
point the menu item "Add As (x,y)" will be enabled.
Once we click on this menu choice a point will
be created at the (x,y)
point corresponding to the measures selected and their relative
distances
on the axes in relation to the unit x-distance at point B. In the
figure
below we see that when the radius is about 1.5 the (x,y) point will be
located at approximately 1.5 along the x-axis, and the y value will be
at approximately 7.25 along the y-axis. As we change the radius
of
the circle the measurements and the (x,y) point will update themselves
accordingly.

Add
Point on Function from x-Point: Use this option to add a new point
to the graph of an existing function y=f(x). For example,
suppose we have constructed the graph of f(x) = x^2
and have plotted a point A somewhere in the plane. If we select
the point and the graph, this menu item will become enabled and
choosing this option will create a point B on the graph that will track
the x-coordinate of B.

Iterate
function from Point...: Use this option to
automate the iteration of a function on an initial point. In the figure
below, we first constructed the graph of f(x) = x^2 and the point A. If
we select A and the graph, this menu option will be enabled. Choosing
this menu item will bring up a dialog box asking for the iteration
level. We set this example at 2. Once we hit okay in the dialog box,
the points B, C, D, and E will be created. B is the image of the
x-coordinate of A on the graph of f(x). C is the point on y=x (the
green line) associated to B. Essentially, by plotting C we can use the
y-value of B as the next x-value. Point D is then the f(x) value
associated to the x-coordinate of C. Again, we move over to y=x
yielding point E. This process can be continued again and again,
yielding f(x), f(f(x)), f(f(f(x))), etc.

Misc Options:
Derivative of
Function: Use this menu option to compute
the derivative of a function. Select the graph of a function and choose
this menu item. The graph of the derivative will then be plotted.
Input Box for Function: Use this menu option to create an
onscreen textbox for
changing the value of a function definition. Select the graph of a
function to enable this option. In the figure below we have
created the graph of f(x) = x^2, and an input box for the function. At
this point we could type in a new definition.
Here we changed the definition to cos(x).