CGRAPH - Mathematische Grafiken

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====== Real plane : Functions ======
The representation of [[https://en.wikipedia.org/wiki/Function_(mathematics)|functions]] in two-dimensional space is the oldest area within the mathematical application of computer graphics. CGRAPH provides the routines required for curve discussion.

{{screen_EN:scr_functions.png}}

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. 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 **//Define drawing area//** checkbox, you can select your own area - the function will then only be drawn for x within this area.

In addition to the function, its [[https://en.wikipedia.org/wiki/Differential_calculus|first and second derivatives]] and the [[https://en.wikipedia.org/wiki/Integral_calculus|definite integral]] can also be displayed. The calculation is performed graphically based on the calculated values for the function. The drawing is done in different colours, which can be adjusted afterwards. You can find out more about curve sketching [[https://en.wikipedia.org/wiki/Curve_sketching|here]]

Zero points and extreme values of the function can also be plotted. These are represented by small squares around the respective point, which are in the same colour as the corresponding graph – zero points in the colour of the function, extreme values in the colour of the first derivative and inflection points in the colour of the second derivative.

After clicking on the **//Create graph//** button, CGRAPH switches to the **//Graphics//** tab and displays the graph. 

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The default values can be viewed in the tree on the left-hand side. Clicking on the (optional) parameter also activates the parameter's adjustability at the bottom. An explanation of this function can be found in the [[BedienungParameterR|notes on changing the parameter in the graphic display]]. 

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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 function, etc. allows you to quickly hide the graphic from the display. Double-clicking on the text allows you to adjust the [[Stroke2D|graphical representation]].

The **//Export//** button allows you to create a file in semicolon-separated [[Exportformat|CSV format]]; the x-values and the corresponding function values are exported. If not only the function but also derivatives or the integral are drawn, these are also exported in separate files.

The exported values can be re-used within CGRAPH, for example in [[linearalgebra2d|linear algebra]] or for [[interpolations]].

[[Operating_the_Graphics|Notes on operating the graphic display]]

[[RealPlane|Back to overview]]