Continuity is a configurable applet that extends the SimpleGraph applet. Like SimpleGraph, it shows the graph of a function and, optionally, marks a point on the graph. If there is a point, then the user can control its x-coordinate either by adjusting a slider at the bottom of the applet or by entering the x-coordinate in an input box. Continuity extends this by supporting the display of open and closed points and dashed asymptote lines on the graph as part of the examples. Its default configuration, with no params, looks just like SimpleGraph. You can also add a tick mark to the x and y axes, with corresponding input boxes and labels. This might be used for showing the c and L points on an applet that explains labels. The location of the ticks is specified in an example string. If you use the x tick option, you can also add a table to the applet that show values near the x tick.
Here is the same applet, configured using a variety of applet params. There is a menu of examples at the top of the apple that the user can load, some of which show points or asymptotes. The parser has also been configured so that you can leave out the "*" operator in multiplication. "Mouse zooming" has been turned on. You can "zoom" by clicking, shift-clicking, or clicking-and-dragging on the canvas. "Panning" has been turned on, so you can right-click-and-drag to drag the graph. A "Restore" button has been added to the LimitsControlPanel to make it easy to get back to the original limits after a sequence of zooms.
The applet tag that creates the applet is as follows:
<applet archive="webcompmath.jar" code="net.sourceforge.webcompmath.applets.Continuity"
<param name="UseMouseZoom" value="yes">
<param name="UsePanner" value = "yes">
<param name="UseRestoreButton" value="yes">
<param name="OptionalStars" value="yes">
<param name="Essential Discontinuity; 1/(x-1);;asymptote,1,0,1,1">
<param name="Example2" value="Jump Discontinuity;(x<1?1:2);;open,1,1;closed,1,2">
<param name="Example3" value="Removeable Discontinuity;x(x-1)/(x-1);;open,1,1">
Most of the applet params are processed by the source code in the classes SimpleGraph and GenericGraphApplet. See SimpleGraph and the list of generic params for that class for information about those parameters. The only param difference is in the syntax of the Example params.
Param Name Type Default Description XTick String (none) If set to a value, such as "c", this will cause a label and tick mark to be added to the graph on the x-axis. An input box is also added at the bottom of the applet to control the position. The tick is only shown if a value is specified for it in an example. YTick String (none) If set to a value, such as "k", this will cause a label and tick mark to be added to the graph on the y-axis. An input box is also added at the bottom of the applet to control the position. The tick is only shown if a value is specified for it in an example. UseTable yes/no no If set to yes, adds a table of values to the applet, to the left of the graph. The table is only shown if a value is specified for the xtick in an example. Example,
String (none) These params can be used to define examples that are presented to the user in a menu at the top of the applet. You can use "Example1" whether or not you use "Example". However, to use "Example2", you must also use "Example1". To use "Example3", you must also use "Example2". And so forth. The value should be a string with elements separated by ";". The part of the string before the first ";" appears in the example menu as a name for the example. The second element is a list of four or five numbers separated by commas. The first four numbers represent the xmin, xmax, ymin, and ymax limits. The fifth number (optional) is the location of the crosshair.
If there are more semicolons and elements, each such element is a comma separated list. For open points, the first item is "open" and the next two items are the x,y coordinates of the point. Closed points are similar, except that the first item is "closed". Line asymptotes use "asymptote" as the first item, followed by four numbers representing the x,y coordinates of two points on the line. You can also add an element to set the x tick and y tick locations by setting the first item to "xtick" or "ytick" and the second to a number representing the location of the tick.