y=k/x=k 1/x

xy=k

y=k x^- 1

Y=k\x(k is a constant and x is not equal to 0). Properties of inverse proportional function: 1. When k >; 0, the images are located in the first and third quadrants respectively; When k < 0, the image is located in the second and fourth quadrants respectively.

2. When k>0 is in the same quadrant, Y decreases with the increase of X; When k < 0, y increases with the increase of x in the same quadrant.

K>0, function in x

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

3. Because in y=k/x(k≠0), neither X nor Y can be zero, and the image of the inverse proportional function cannot intersect with the X axis or the Y axis.

4. In the inverse proportional function image, take any two points P and Q, the intersection points P and Q are parallel lines of the X axis and the Y axis respectively, 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 symmetrical axes y=x y=-x (that is, the bisectors of the first, third and fourth quadrants), and the symmetrical center 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 the signs of m and n are the same), then the two points A and B 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 b? +4k m≯ (not less than) 0.

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