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
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Examples
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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
- Vertical shifts:
f1(x)=x2,
shifted: up 2, up 4,
down 2, down 4
- Horizontal shifts:
f1(x)=x2,
shifted: right 2, right 4,
left 2, left 4
- Addition:
f1(x)=x2,
f2(x)=x+1,
f3(x)=
f1(x)+f2(x)
- Subtraction:
f1(x)=x2,
f2(x)=x+1,
f3(x)=
f1(x)-f2(x)
- Multiplication:
f1(x)=x2,
f2(x)=x+1,
f3(x)=
f1(x).f2(x)
- Division:
f1(x)=x2,
f2(x)=x+1,
f3(x)=
f1(x)/f2(x)
- Composition:
f1(x)=ex,
f2(x)=x2,
f3(x)=
f1(f2(x))
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.