The Display menu contains the commands "As Expression", "As Graph", "As Table", "As Diagram", and "As Black Box", as well as three commands dealing with graph displays. The commands for graph displays are described in the Help menu entry "Special Graph Operations." The first five commands are described here. These commands control how a function is exhibited in a display window. If the active window is not a function display window, then none of the commands are available. In addition, the commands As Expression and As Diagram are available only if the function displayed was originally defined as an expression.
When you create a new function, when you double-click on a function name in the function list window, or when you hilite a name in that window and choose Open from the Function Menu, a window is opened in which the definition of the function is displayed. When you first open a display window, the function is shown in the same form in which it was defined (expression, graph, or table). You might prefer to see a particular function as a graph, or you might want to see a table of input/output pairs.
The As Graph command will cause the graph of the current function to be displayed. (For a function defined as an expression, you can change the limits on the x and y axes using the Set X,Y Limits command from the Function menu.)
The As Table command will display a list of input/output pairs. Each entry in the table represents the (x,y) coordinates of a point on the graph of the function. If the function was defined as a graph, equally spaced x-values across the domain of the function are used. For a function defined as an expression, approximately 50 points are displayed with x-values evenly spaced from some minimum to some maximum; these limits can be set using the Set Parameters command from the Function menu. (If you have specified an "optional cluster point" using the Set Parameters command, the x-values are generated differently: 21 values are displayed clustered near the specified cluster point.)
The As Black Box command will collapse the window to its minimum vertical size, so that only the input and output boxes at the top of the display are visible. You can still type in an input and see the corresponding output, but you can't see the definition of the function. (That is essentially what is meant by a "black box.")
For a function defined as an expression, the As Diagram command will display the function in a rather unusual but interesting form. It contains the same information contained in the expression that defines the function, laid out in two dimensions to make clear the steps in computing the output from the input. The diagram consists of boxes joined by lines. The boxes hold numbers; a line represents a computation and is marked with the function or operator that does the computation. The computation flows from left to right, with the value in a box at the right end of a line being computed from the data in the box or boxes on the left end of the line. If this is not clear, try it out with an expression such as 3*x+sin(x). Define this function, change its display style to As Diagram and type in some value for x. The diagram will show how the value of the expression is computed. (Diagrams of all but fairly simple functions will be too large to fit on the screen. You will be able to scroll all parts of the diagram into view, but this will probably not be very satisfactory.)
