First, draw the function image directly.

Open the geometry sketchpad software, and click "Draw New Function" under the "Drawing" menu to pop up the input box on the right. For example, we want to draw the function y=2x+3 once: enter 2x+3 in the input box, select y in the equation button, and then click OK to automatically generate the function image in the drawing area (as shown in figure 1).

This function image is full screen, and the plane rectangular coordinate system has no positive direction, and the system plane rectangular coordinate system also has its own grid, so I seldom use this method to draw function images.

Second, draw a function image with parameters.

Similarly, to draw an image with the function y=2x+3, we can establish parameters before drawing the image: click New Parameter under the data menu, change the name to K in the pop-up box, fill in 2 data, press OK button, then establish parameter b=3, and then click Draw under the drawing menu.

To draw a function image in this way, you can use the coordinate system in the "User-defined Tool" after the parameters and functions are built, for example, choose "Non-parametric version of Flying Fox" to establish a plane rectangular coordinate system, then click "Function Generation Tool" and click the function y=kx+b, and the image will be generated.

The value range of the independent variable x of the generated function image is related to the abscissa of the coordinate system, which can avoid full screen. (as shown in figure 2)

Third, draw a function with trajectory.

Open the geometry sketchpad software, and take "Flying Fox Non-parametric Edition" as an example. First, establish a plane rectangular coordinate system, take any point on the abscissa, measure the abscissa value of that point, change the label in the attribute to X, then click Calculate under the Data menu, enter: 2, measured value,+,3 in the pop-up box in turn, click OK, and then put the label in the attribute. The latter inputs the calculated value, and after pressing the "Draw" button, the corresponding point will be automatically generated in the coordinates. Click the drawing point and moving point on the abscissa in turn, and then click Trajectory under the Construction menu to draw the function image (as shown in Figure 3).

Fourthly, the subsequent functions are drawn by user-defined transformation.

This method of drawing function image is similar to drawing function image with trajectory. Firstly, establish a plane rectangular coordinate system (flying fox without reference), take a line segment AB on the abscissa, then take any point C on the line segment AB, measure the abscissa value of the point C, change the label to X, calculate the value of 2x+3, change the label to Y, take the values of X and Y as horizontal and vertical drawing points, and select the drawing point and moving point C on the line segment AB in turn. Click Create User-defined transformation under the transformation menu, click OK, connect AC with line segment tool, click drawing point and line segment AC again, and select transformation 1 under the transformation menu to generate subsequent functions. The image of this function will change with the change of point C (as shown in Figure 4).