1, the concept of inverse proportional function

Generally speaking, a function (k is a constant and k0) is called an inverse proportional function. The analytical expression of inverse proportional function can also be written as. The value range of the independent variable X is all real numbers of x0, and the value range of the function is also all non-zero real numbers.

2. Inverse proportional function image

The image of the inverse proportional function is a hyperbola, which has two branches, which are located in the first and third quadrants, or the second and fourth quadrants respectively, and they are symmetrical about the origin. Because of the independent variable x0 and the function y0 in the inverse proportional function, its image does not intersect with the X axis and the Y axis, that is, the two branches of the hyperbola are infinitely close to the coordinate axis, but they will never reach the coordinate axis.

3. The properties of inverse proportional function

When k>0, the two branches of the function image are in the first and third quadrants respectively. In each quadrant, y decreases with the increase of x.

4. Determination of inverse proportion of resolution function.

The method of determining sum is, er, the undetermined coefficient method. Because there is only one undetermined coefficient in the inverse proportional function, only a pair of corresponding values or the coordinates of a point on the image can be used to find the value of k, thus determining its analytical formula.

5. Geometric meaning of inverse proportional function

Let it be any point in the inverse proportional function image, and the intersection point P is the vertical line and vertical foot A of the axis, then the area of △OPA is the area of rectangular OAPB. This is the geometric meaning of the coefficient. And no matter how P moves, the area of △OPA and the area of rectangular OAPB remain unchanged.