### Combinations and Transformations of Functions

Graphs up to 5 functions simultaneously in rectangular coordinates, allowing definitions of one function in terms of others.
How to use   ||   Examples   ||   Other Notes

How to Use
• Enter a function f1(x) in the text input field marked "f1(x)=" (Example: f1(x)=ex)
• Click the "Graph" button (this button also refreshes the graph)
• To see two functions graphed simultaneously:
• Enter the second function f2(x) in the text input field marked "f2(x)="
• Click (to its "on" state) the check box next to this input field
• Click the "Graph" button
(Example: f1(x)=ex and f2(x)=x2)
Up to 5 functions can be graphed simultaneously
• A function can be defined in terms of another function -- for example, to define f2(x) using the function f1(x), such as f2(x)=f1(x)+2, you can type "f1(x)+2" in the text input field marked "f2(x)=".
(Example: f1(x)=x2 and f2(x)=f1(x)+2)
• To remove a function from the graph, click (to its "off" state) the check box next to the associated text input field and click the "Graph" button to refresh
• To erase the graph and all input fields, click the "Clear" button
The text input fields can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates.
Examples

Other Notes
The graphs of the functions are color-coded, corresponding to the colors of the labels marking the text input fields: the graph of f1(x) is blue, f2(x) is red, f3(x) is green, f4(x) is orange, and f5(x) is magenta.

In order to avoid recursion-related problems, a function cannot be defined in terms of itself -- for example, trying to define f1(x)=f1(x)+5 will generate an error, shown similar to a syntax error (the text input field will be highlighted). This check for recursion is not very sophisticated, and can be easily subverted by specifying a circular chain of function definitions, but in that case the applet will generate a Java stack overflow exception and no graph will be generated.