The range of the independent variable x is all real numbers that are not equal to 0.

Inverse proportional function image properties:

The image of the inverse proportional function is a hyperbola.

Since the inverse proportional function belongs to odd function, let f(-x)=-f(x), and the image is symmetrical about the origin.

In addition, from the analytical formula of inverse proportional function, it can be concluded that any point on the image of inverse proportional function is perpendicular to two coordinate axes, and the rectangular area surrounded by this point, two vertical feet and the origin is a constant, which is ∣k∣.

As shown in the figure, the function images when k is positive and negative (2 and -2) are given above.

When k > 0, the inverse proportional function image passes through one or three quadrants, which is a decreasing function.

When k < 0, the inverse proportional function image passes through two or four quadrants, which is increasing function.

The inverse proportional function image can only move towards the coordinate axis infinitely, and cannot intersect with the coordinate axis.

Knowledge points:

1. Any point on the inverse proportional function image is a vertical line segment of two coordinate axes, and the area of the rectangle surrounded by these two vertical line segments and coordinate axes is | k |.

2. For hyperbola y = k/x, if you add or subtract any real number on the denominator (that is, y = k/(x m) m is a constant), it is equivalent to translating the hyperbola image to the left or right by one unit. (When adding a number, move to the left, and when subtracting a number, move to the right)

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Proportional function

If y=kx(k is constant and k is not equal to 0), then y is called a proportional function of X. 。

Proportional function also belongs to linear function.

Image exercise: 1. The constant coefficient is 2. Tracking point 3. Connecting line (must pass through the origin of coordinate axis).

Others: When k>0, its image (except the origin) is in the first and third quadrants, Y increases with the increase of X.

When k < 0, its image (except the origin) is in the second and fourth quadrants, and y decreases with the increase of x.

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Listen carefully in class ~