(k is a constant, k≠0), then y is said to be an inverse proportional function of X.

Because y=k/x is a fraction, the range of the independent variable x is X≠0.

The inverse proportional function image belongs to a central symmetric hyperbola with the origin as the symmetric center.

Each curve of each quadrant in the inverse proportional function image will be infinitely close to the X axis and the Y axis, but will not intersect with the coordinate axis (K≠0).

Properties of inverse proportional function

1. when k>0, the image is located in the first and third quadrants respectively, and in the same quadrant, y decreases with the increase of x; When k < 0, the image is located in the second and fourth quadrants respectively, and in the same quadrant, y increases with the increase of x.

2.k>0, function in x

The domain is x ≠ 0; The range is y≠0.

3. Because in y=k/x(k≠0), X can't be 0 and Y can't be 0, so the image of inverse proportional function can't intersect with X axis or Y axis.

4.

In the inverse proportional function image, take the intersection of any two points P, Q and P, Q as parallel lines of X axis and Y axis respectively, and the rectangular area enclosed with the coordinate axis is S 1, S2 is S 1=S2=|K|.

5.

The image of inverse proportional function is not only an axisymmetric figure, but also a centrally symmetric figure with two axes of symmetry.

y=x

Y=-x (that is, the bisector of the first, third and fourth quadrant angles), and the center of symmetry is the coordinate origin.

6. If the positive proportional function y=mx and the inverse proportional function y=n/x intersect at two points A and B (M and N have the same sign), then A

Two points are symmetrical about the origin.

7. Let there be an inverse proportional function y=k/x and a linear function y=mx+n on the plane. If they have a common intersection, then n 2+4k m ≥ (not less than) 0.

8. Inverse proportional function y = k/x: asymptote of X axis and Y axis.

9. The inverse proportional function is symmetric about the positive proportional function y=x, y=-x, and symmetric about the origin center.

10. On the inverse scale, point M is perpendicular to X and Y respectively, and intersects with Q and W, then the area of rectangular mwqo(o is the origin) is |k|.

The inverse proportional functions with equal 1 1.k value coincide, and the inverse proportional functions with unequal k values never intersect.

12. The larger the | k |, the farther the image of the inverse proportional function is from the coordinate axis.

13. The inverse proportional function image is a central symmetric figure, and the symmetric center is the origin.