The commands in the Function menu are "New Function", "Open Function", "Close Window", "Modify Function", "Delete Function" and "Set X,Y Limits".
Use the New Function command whenever you want to define a new function. You will be presented with a dialog box in which you can specify the name of the function you want to define and whether it is to be defined as an expression, as a graph, or as a table of input/output pairs. The name can contain letters, digits, and the underscore character "_". It must begin with a letter. Note that the name of a function would be, for example, "fred" rather than "fred(x)". When you have entered the name and selected the type of function, press return or click the OK button. (Click the Cancel button if you decide you don't want to create a new function after all.)
You will be presented with another dialog box in which to enter the function definition. There is a different box for each type of function. Each of these boxes has an OK button, a Cancel button and a Revert button. Press return or click on OK when you have finished the function definition. If you decide to abort entering the function, click on Cancel. The Revert button will eliminate any changes you have made and restore the dialog box to the state it was in when it first appeared.
When entering a function as an expression, you have the option of specifying a domain for the function. For example, you can define a function to be x^2+1, provided x > -1. You can also specify a "split function" that has different definitions on different parts of its domain. See the Info Menu entry Typing Expressions for more information.
You can enter a graph by drawing it with the mouse. Because of the finite resolution of the screen, this will actually just specify a certain number of points (about 150) on the graph. The actual function will be a smooth curve, with a continuous derivative. (In case you are familiar with such things, the program uses "cubic spline curves" to find the value of the functions between the points specified.) Since the result of your drawing will look very jagged (and will have pretty wild first and second derivatives), a Smooth button is provided which will make the graph a little smoother. I suggest that you click on this a few times after finishing your graph. The window for entering graphs contains boxes where you can type minimum and maximum values for x and y. These specify the ranges for x and y represented by the rectangle in which you draw the graph. The lower left corner of the rectangle is the point (xmin,ymin) and the upper right is (xmax,ymax). Xmin and xmax determine the domain of the function.
The dialog box for table entry has an area in which you can enter input/output pairs for the function. Another way of saying this is that you are entering x and y coordinates of points on the graph of the function. The dialog box contains instructions on how to enter such points.
The domain of the function defined by your table extends from the minimum x value to the maximum x value among all the points you enter. When the function is graphed or used in the definition of another function, there must be some way of deciding the value of the function for x-values between the x-values you specify in the table. You have two options for how this can be done. You can specify that the function is continuous, and in that case, the function will be defined by joining the points you enter by straight line segments. Or, you can specify a step function, and in that case, the function will be constant on intervals between your specified x-values. The value of a function on an interval is defined by the y-value at the left-hand endpoint of the interval. (It would make sense for the y-values of the last two points that you define to be the same, but this is not required.)
For any of the function definition styles, when you finish the definition of the function, a new window will be opened in which the definition of the function will be displayed.
The Open Function command is available when the function list window is the active window and one of the functions in the list is hilited. This command will open a display window for the function. The same effect can be achieved by double-clicking on the function name, so this command is rarely used.
The Close Window command is available when the active window is a function display window. It will close the window. The same effect can be achieved by clicking in the window's close box, so this command is rarely used.
The Modify Function command is available when the active widow is a function display window or when the active window is the function list window and one of the functions is hilited. This command allows you to change the definition of the function. You will be presented with the same dialog box that was used to define the function, initialized with the current function definition. You can make any changes you like and save the new definition. (It is not possible to change the type of function, from an expression to a graph, for example.) Use the Cancel or Revert button if you make a mistake or if you decide that you don't want to change the definition of a function after all. Note that modifying a function used in the definitions of other functions will indirectly change those functions as well.
The Delete Function command is available under the same circumstances as Modify Function. It is used to delete a function from the list of available functions. It will close any display windows open for that function before removing the function. You will not be allowed to delete a user-defined function that is used in the definition of another function. Note that the standard, predefined functions such as tan(x) and ln(x), can still be used in expressions even if they have been deleted from the function list. Also, you can delete them from the list even if they are used in the definitions of other functions.
The Set X,Y Limits command applies only to functions defined as expressions. It is available when the active widow is the display window for such a function, or when the function list window is active and such a function is hilited. This command affects how the function is displayed as a table or as a graph. You can specify the minimum and maximum x-values to be used for the table or graph. You can also specify minimum and maximum y-values to be used on the y-axis of a graph. If you leave one of these blank, a value will be computed for you. (The result might not look good; it is often best to allow the computer to generate the initial values for ymin and ymax and then reset them to make the graph look better.)
