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# Functions and Curves The program can display functions and parametric curves in the construction, or use user defined functions of one or more parameters in other expressions. It is also possible to display the zero set of a function of two variables.

First, we describe the type of functions for display in the construction window. In the dialog, enter the start and stop value of the parameter variable and the step size. If you wish, you can use any string not containing blanks as a parameter name. The default is "x". For a function, leave the X-value empty or set it to "x", and enter an expression dependong on "x" for the Y-value. For a parametric curve, one needs two expressions, one for the X-value and one for the Y-value.

The program will increment the parameter variable from start to end using the given step size. If the function is valid between two parameter steps, a line segment is drawn in the construction using the construction coordinates.

This type of functions can be used in other functions. The Y-value will be evaluated then.

Functions and curves can be filled. For a parametric curve, the center is 0, but can be changed. To do that use the properties dialog and press the "Select Center" button. Functions can be reduced to a sequence of points. If a function is filled additionally, a Riemann step function will be drawn.

Display functions or curves can intersect with other objects, and points can be fixed on the function graph. Geometrically these functions behave like a curve.

User defined functions of several variables cannot be plotted. Their purpose is to be used in other expressions. Consequently, there is a much simpler dialog for these functions, which can be called by holding the ctrl-key while pressing the function icon. One has to declare all variables, separated by blanks, in this dialog. The variables may then be used in the expression. There is only one expression, of course. The function will display its definition, unless it is hidden, of course. The display can be moved as usual.

The program can plot and display the zero sets of user defined functions in two dimensions. There is a switch in the settings dialog to show this set. Use any two variables and an expression in these variables.

Related topics: Syntax for Expressions, Object Properties

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