# Documentation

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# funtool

Function calculator

## Syntax

```funtool ```

## Description

`funtool` is a visual function calculator that manipulates and displays functions of one variable. At the click of a button, for example, `funtool` draws a graph representing the sum, product, difference, or ratio of two functions that you specify. `funtool` includes a function memory that allows you to store functions for later retrieval.

At startup, `funtool` displays graphs of a pair of functions, `f(x) = x` and ```g(x) = 1```. The graphs plot the functions over the domain ```[-2*pi, 2*pi]```. `funtool` also displays a control panel that lets you save, retrieve, redefine, combine, and transform `f` and `g`.

### Text Fields

The top of the control panel contains a group of editable text fields.

 f= Displays a symbolic expression representing `f`. Edit this field to redefine `f`. g= Displays a symbolic expression representing `g`. Edit this field to redefine `g`. x= Displays the domain used to plot `f` and `g`. Edit this field to specify a different domain. a= Displays a constant factor used to modify `f` (see button descriptions in the next section). Edit this field to change the value of the constant factor.

`funtool` redraws `f` and `g` to reflect any changes you make to the contents of the control panel's text fields.

### Control Buttons

The bottom part of the control panel contains an array of buttons that transform `f` and perform other operations.

The first row of control buttons replaces `f` with various transformations of `f`.

 df/dx Derivative of `f` int f Integral of `f` simplify f Simplified form of `f`, if possible num f Numerator of `f` den f Denominator of `f` 1/f Reciprocal of `f` finv Inverse of `f`

The operators int f and finv can fail if the corresponding symbolic expressions do not exist in closed form.

The second row of buttons translates and scales `f` and the domain of `f` by a constant factor`.` To specify the factor, enter its value in the field labeled a= on the calculator control panel. The operations are

 f+a Replaces `f(x)` by `f(x) + a`. f-a Replaces `f(x)` by `f(x) - a`. f*a Replaces `f(x)` by `f(x) * a`. f/a Replaces `f(x)` by `f(x) / a`. f^a Replaces `f(x)` by `f(x) ^ a`. f(x+a) Replaces `f(x)` by `f(x + a)`. f(x*a) Replaces `f(x)` by `f(x * a)`.

The first four buttons of the third row replace `f` with a combination of `f` and `g`.

 f+g Replaces `f(x)` by `f(x) + g(x)`. f-g Replaces `f(x)` by `f(x)-g(x)`. f*g Replaces `f(x)` by `f(x) * g(x)`. f/g Replaces `f(x)` by `f(x) / g(x)`.

The remaining buttons on the third row interchange `f` and `g`.

 g=f Replaces `g` with `f`. swap Replaces `f` with `g` and `g` with `f`.

The first three buttons in the fourth row allow you to store and retrieve functions from the calculator's function memory.

 Insert Adds `f` to the end of the list of stored functions. Cycle Replaces `f` with the next item on the function list. Delete Deletes `f` from the list of stored functions.

The other four buttons on the fourth row perform miscellaneous functions:

 Reset Resets the calculator to its initial state. Help Displays the online help for the calculator. Demo Runs a short demo of the calculator. Close Closes the calculator's windows.