Welcome to the program "xFunctions." This program allows you to define and view functions in various ways. It also provides a number of utilities for doing various interesting things with functions.
When you think of functions, you probably think of functions defined as mathematical formulas, such as "f(x) = 3*x^2 + 1/x." However, this is only one type of function. In general, a function f(x) can be any rule for taking one number, x, as input and producing another number, f(x), as output. For example, a function can be specified by drawing a graph or by giving a table of input/output pairs. xFunctions allows you to define a function by giving an expression, a graph, or a table. Functions can also be displayed in various forms. Any function can be displayed as a graph or a table. This program can also display a function defined by an expression in a more unusual form, called a diagram. A diagram exhibits all the steps in computing the output value of the function from the input value.
The window titled "List of Functions" contains a list of names of functions that have been defined and that are available for use in expressions. If you double click on one of the function names (or click once to highlight it and then choose Open from the Function menu), the function will be displayed in a new window. You can use the display menu to control the way a function is displayed. You can open several windows for the same function, with different displays of the function in each window.
Each function display window has two rectangles at the top, labeled Input and Output. You can type a number into the Input box of the active window. The Output box will always show the corresponding output of the function for that input (provided the input is a legal number in the domain of the function). For a graph, the corresponding point on the graph will be indicated by a dotted line drawn to each axis. For a diagram, all the intermediate results of the computation will be shown in the diagram.
The Info menu contains an entry for each of the other menus used in this program. These entries describe the commands provided by the menu and discuss the things you need to know to use those commands. It also contains entries describing the seven "utilities," Multigraph, Animate, Derivatives, Riemann Sums, Parametric Curves, Integral Curves and 3D Graph; these utilities allow you to play with functions in particular ways.
The Info menu entry "Typing Expressions" explains the rules for typing expressions in the standard computer notation that you must use in this program.
The entry "Special Graph Operations" describes some special features provided for working with a function display window that is displaying a graph.
You should also take a look at the Info entry "Never Trust a Computer," which contains some advice and warnings about how to interpret what you see on the screen when you run this (or any) computer program.
