Real plane : Function families
A function can be superimposed multiple times by varying a parameter using the Functions graphic. This is easier with function sets, which vary the parameter with a single call and can thus display several function curves at once.
By definition, functions in two-dimensional space (R²) can only depend on one variable. Therefore, only functions containing the variables x and param are permitted, whereby param is mandatory. Enter the desired function in the input field for the function, or select one of the existing functions by clicking on the arrow to the right of the input field.
CGRAPH displays functions within the area visible in the graph for the variable x. By activating the checkbox Define drawing range, you can select your own range – the function will then only be drawn for x within this range.
In the Parameters and iterations area, you can specify how the parameter is to be varied and how many functions are to be drawn (maximum 20). If the checkbox Allow only integer parameters is activated, only the lower parameter value can be changed – the upper value adjusts automatically based on the number of iterations selected.
CGRAPGH can automatically display function sets in different colours if the corresponding checkbox is selected. Any change to the general colour in the tree view will then be ignored.
After clicking the Create graph button, CGRAPH switches to the Display tab and displays the graph.
The default values can be viewed in the tree on the left-hand side. Clicking on the (mandatory) parameter also activates the parameter's adjustability at the bottom. An explanation of this function can be found in the notes on changing the parameter in the graphic display.
The values can be changed retrospectively – clicking on one of the values switches CGRAPH back to the tab with the default values. The graphic is adjusted as soon as the Create graphic button is clicked. Clicking on the coloured symbol for the graph allows you to quickly hide the graphic from the display. Double-clicking on the text allows you to adjust the graphical display.
The Export button allows you to create a file in semicolon-separated CSV format; the x-values and the corresponding function values are exported. If not only the function but also derivatives or the integral are plotted, these are also exported in separate files.