In the image and properties of inverse proportional function in the second section of inverse proportional function, the textbook lists three inverse proportional functions, y=2/x, y=4/x and y = 6/x. It is necessary to observe their images and find their * * * same characteristics (page 150 of the textbook). At the same time, in order to guide students to think,

Features: When k>0, hyperbola is in the first and third quadrants, symmetrical about the origin center and symmetrical about y=x; Then, the second characteristic: in each quadrant, y decreases with the increase of x, which is forced in each quadrant because the independent variable x is not 0. The third feature: the hyperbola is infinitely close to the coordinate axis. The inspiration for this function comes from question 3. After all, it is intuitive whether it intersects with the X axis and the Y axis.

Understand; Understanding

In junior high school, the mathematical description of distance is based on the concept of distance, while the initial distance, the length of the line segment between two points and all subsequent concepts related to distance are based on the distance between two points, such as the distance from a point to a straight line, and the vertical line segment makes a straight line after this point.

The distance between this point and the vertical foot is called the distance between a point and a straight line, such as the distance between parallel lines, that is, the distance between any point on a straight line and another straight line. Even after learning the positional relationship between a point and a circle, distance is the distance between a point and the center of a circle, and so on. Basically, when it comes to distance, it will eventually come down to the length of the line segment between points.