## How to Use the 'GX2' Applet |
see also our special-purpose
Mathlets, Mathlabs, and Modules |

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Graphs | Functions | Variables | Colour | Region | Mouse |

**The 'Graphs' pane is
where
you can tell the applet what to plot.**

Clicking on the 'New Graph' button pops up a
text
box in which you can enter an equation to plot.

The simplest case would be of the form "`y=..`."
where "..." is an expression involving "`x`". When you complete
the entry (by pressing the Enter key) the graph will be displayed. Try
this with something like "`y=x^2-2x`" for example. __[Note__:
If you enter just "x^2-2x" it will assume you mean "y=x^2-2x".]

Other possibilities that are recognized include more general
equations
in `x` and `y` as well as equations in polar
coordinates.
(At present '`r`' is used for the radius and '`theta`'
for the
angle but this choice will soon be made a user option)

You can also enter pairs of parametric
equations
separated by **semicolons**. For example, entering "`x=t^3-t;
y=t^2`"
produces a simple loop graph. (The default domain is from t=-1 to 1,
but
you can change that by adding the domain limits after a second
semicolon.
So for example "`x=t^3-t; y=t^2; -2,2`" gives an extension of
the
loop.)

If you include letters other than '`x','y',or
'r'`
in the equation, they will be considered as parameters (unless
occurring
as parts of longer names or already defined as function names - see
below),
and controls to adjust their values will be presented in the
'Parameters'
pane.

The 'Variables' tab
is attached to a pane where you can define and control named variables

This pane has three parts whose sizes can be adjusted by sliding
the dashed lines up and down.

(In the top section you can rename the 'Coordinates'
but at present the axis labels don't properly reflect this, and the
bottom section called 'Dependent
Variables' is not yet functional, so it is the middle **'Parameters' **section that is most useful)

**The 'Parameters' pane
is where you can define and control numerical constants.**

If you include letters other than already
defined names in a formula, they will be considered as parameters.

Any parameters identified in an input
formula
will have a value controler added in the 'Parameters' pane. This
consists
of a text field where you can explicitly type in a numerical value, a
slider
for adjusting that value, and a pair of buttons labelled with
"><" and
"<>" for "zooming in" and "zooming out" (ie decreasing or
increasing
the range covered by the slider).

It is also possible to force the parser to
recognize
longer variable names by using the 'AddNewParam' button to add new
parameters
before they are used.

**The 'Functions'
tab pulls up a pane
where you can define additional named functions.**

In addition to recognizing the usual functions
of elementary calculus, the parser will also recognize any function
name
defined in this window. Clicking on the 'NewFunction' button brings up
a text field primed with the string "`fn(x)=`" (where `n `is
the number of times the button has been clicked on). This can be
completed
or amended to produce any equation of the form "`functionName(inputName)=expression`"
and on pressing Enter will define a function with the specified
name.
(For example, entering "`f(q)=q^2`" will allow `f(x)` to
replace `x^2`, and `f(t)` to replace `t^2 `in
the
graph definition examples.)

__[Note__: Unlike the original
GraphExplorer, functions are not automatically graphed in this applet.
Rather they become available for use in graph definitions. The 'Graphs'
pane is where you can enter equations and formulas to be graphed.]

**The 'Colour' pane is
where
you can colour a selected object.**

Initially inactive, it becomes available when
a graph's 'Color' button is clicked, or when a plotted object is
clicked
with the right mouse button with the 'alt' key down (ie 'alt-meta'
mouse
clicked on single button systems). The sliders adjust the mix of RGB in
the color and the 'done' button shuts down the ColorSelecter. (It will
pop back again when another color request is initiated).

**Controlling the Region
Displayed**

The region controller used here is as in the
original
GraphExplorer (though the library does include other options). The
mid-point
coordinates and view dimensions can be adjusted by direct input or by
using
the zoom and pan buttons. It is also possible to use the mouse to move
the grid by using a Shift-drag operation.

**Mouse Actions in the
Plot
Pane**

In addition to moving the region with a Shift-drag, the mouse can also be used to display labels and other objects.

Right clicking (or meta-clicking on single button systems) on an item produces an identifying label, and dragging with the right button displays a label with the current coordinates. (And if you want to get rid of it, left clicking on an existing lable makes it go away.)

The control key enables item creation. A control left click adds a plotted point to the display, and a control drag draws a line. Such items can be removed by a ShiftControl left click.

The alt key alters the state of an object. Alt-left click on a line toggles between segment and infinite display, and on a point near a graph 'fixes' it to the graph like a bead on a wire to constrain the effect of future drag operations. Alt-right click on a graph(or alt-meta click for single button systems) brings up a color select panel.

Finally, clicking on a line with Control and
Alt
both pressed creates "run" and "rise" segments to complete the triangle.