Specific methods for designing proportional function images on geometric sketchpad

In daily learning, drawing the image of a proportional function is a common problem. In order to help everyone solve this problem, PHP editor Apple has brought this tutorial to explain in detail the specific method of designing proportional function images on the geometric sketchpad. This tutorial explains it in simple terms and combines pictures and text to allow everyone to easily master the powerful tool of geometric sketchpad, thereby improving the efficiency and accuracy of drawing proportional function images.

Method 1 Geometric method

For example, √2 is the diagonal (hypotenuse) of a right triangle with side length 1, and then use a ruler and compass to draw the drawing on the geometric sketchpad.

Detailed operation: Create a new parameter t1=1, the unit is distance, execute the mark distance command on the parameter; create line segments AB and AC with a length of 1cm; perform the square root calculation of the sum of AB2+AC2, and obtain the value It is the length of line segment BC; it can also be verified by measuring the distance of the three sides. The hypotenuse BC represents √2, and any point on this line segment is an irrational number point.

Method 2 Algebraic calculation

The proportional function is a linear function, but a linear function is not necessarily a proportional function. The proportional function is a special form of a linear function, that is, in the linear function y=kx+b, if b=0, that is, the so-called [intercept on the y-axis] is zero, it is a proportional function.

For example, the proportional function y=2x, the specific operations for drawing its image are as follows:

Step 1 Establish a coordinate system. Open the geometric sketchpad software, press and hold the custom tool button on the left, and select [Classic Coordinate System] - [Ant|Rectangular Coordinate System] in the pop-up shortcut menu to establish a plane rectangular coordinate system as shown in the figure.

Step 2 Enter the analytical expression of the function. Click the [Data] menu above, select the [New Function] command in its drop-down menu, enter the function analytical formula as shown in the pop-up New Function dialog box, and click the [OK] button.

Step 3: The expression of function f(x)=2x will appear on the drawing board. Select it with the right mouse button and select [Draw Function Image] from the pop-up right-click menu. The function image of y=2x can be obtained.

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