One of the intersection coordinates of positive scale function y = KY and hyperbola y = 8 / X is a (2, m). (1) find out the coordinate of point a and (2) find out the relation of inverse scale function (3) Find another intersection coordinate of these two function images

One of the intersection coordinates of positive scale function y = KY and hyperbola y = 8 / X is a (2, m). (1) find out the coordinate of point a and (2) find out the relation of inverse scale function (3) Find another intersection coordinate of these two function images

A (2, m) is on the hyperbola, so we substitute it to get m = 4
A (2,4) in the positive proportion function, substituting 2K = 4, we get k = 2, y = 2x
By combining y = 2x and y = 8 / x, we get x = - 2, x = 2
The other point coordinates are (- 2, - 4)

It is known that the image intersection of positive scale function y = - 4x and inverse scale function y = K / X and two points AB, if the coordinate of a is (x, 4), B is obtained

The solution is obtained from the point a (x, 4) on the positive scale function y = - 4x image
So - 4x = 4
That is x = - 1
So a (- 1,4)
In addition, point a (- 1,4) is placed on the image with inverse scale function y = K / X
That is, K / (- 1) = 4
K = - 4
So the inverse proportion function y = - 4 / X
By y = - 4x and y = - 4 / X
The simultaneous solution is x = - 1, y = 4 or x = 1, y = - 4
So B (1, - 4)

If the value of quadratic function y = - 1 / 3 (x + 2) x & # 178; + 1 decreases with the increase of X, then the range of X is smaller

Since the opening of y = - 1 / 3 (x + 2) & # + 1 is downward and the axis of symmetry is x = - 2, when x ＞ - 2, y decreases with the increase of X