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
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.

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.