The image with positive scale function y = KX passes through point a (k, 2K) (1) Find the value of K; (2) If point B is on the x-axis and ab = Ao, find the analytic formula of line ab

(1) ∵ the image with positive scale function y = KX passes through point a (k, 2K),
ν 2K = K2 and K ≠ 0,
K = 2;
(2) ∵ from (1), k = 2, ᙽ a (2,4) ᙽ OA=
22+42=2
Five
∵ point B is on the x-axis,
If B (T, 0) (t ≠ 0), then
(2-t)2+42=2
5，
T = 0, or T = 4,
∴B（4，0）．
Let y = ax + B (a ≠ 0), then
2a+b=4
4a+b=0 ，
The solution is,
a=-2
b=8 ，
Then the analytic formula of line AB is y = - 2x + 8

The image passing through point a (k, 2K) with positive scale function y = kx Find the value of K

Replace the point a (k, 2K) with y = KX,
2k=k*k
K = 2 or 0
When k = 0, it is not a positive proportional function
K=2

The distance from the intersection point P (m, 4) of the image of inverse scale function and positive scale function is twice the distance of Y axis. Find the coordinates of point P and write the analysis of these two functions

The distance from P (m, 4) to the x-axis is 4
The distance from P (m, 4) to the y-axis is | M|
4=2|m|
M = 2 or - 2
If P (2,4)
Inverse scaling function y = 8 / X
Positive scaling function y = 2x
If P (- 2,4)
Inverse scaling function y = - 8 / X
Positive scaling function y = - 2x

Given the inverse scale function y = 2 / x, there is a point P to X axis in the first quadrant of the image, and the y-axis distance is equal. Find the analytic formula of the positive proportion function passing through the point P

∵ if the inverse scaling function y = 2 / x, there is a point in the first quadrant of the image from P to X axis, and the distance between Y axis is equal
∴X=2／X
∴X=Y=±√2
Point P is in the first quadrant
∴P﹙√2,√2﹚
Let the analytic formula of positive proportional function passing through point p be y = KX
∴√2=√2K
K=1
The analytic formula of positive proportion function passing through point P is: y = X

We know that the distance from the intersection point of the image of positive scale function and hyperbola to X axis is one, and the distance to y axis is two, and their analytic formulas are obtained

The distance from the intersection point to the x-axis is one, and the distance to the y-axis is two
Then the coordinates of the intersection point are: (2,1) or (2, - 1) or (- 2,1) or (- 2, - 1)
In other words, their analytical expressions are as follows:
Y = 1 / 2x and y = 2 / X
Y = - 1 / 2x and y = - 2 / X

It is known that Y-1 is a positive proportional function of x 1, the function value y decreases with the increase of X, and the distance from the intersection point of function image and y-axis to x-axis is equal to 2, then y and X It is known that Y-1 is a positive proportional function of x 1, the function value y decreases with the increase of X, and the distance from the intersection point of function image and y-axis to x-axis is equal to 2, then the functional relationship between Y and X is?

Let Y-1 = K (x-1), then K

It is known that the distance from the intersection point of the image of positive scale function and inverse scale function to x-axis is 3 and the distance to Y-axis is 4. The analytic expressions of these two functions are obtained

Let the analytic formula of positive and negative proportional function be y = K1X, y = k2x (K1 ≠ 0, K2 ≠ 0) and let the image intersection point of two functions be p (x, y), | x | = 4, | y | = 3. When x = 4, y = 3, substituting y = K1X, there are 3 = 4k1, K1 = 34,  y = 34x; when y = k2x, there is 3 = K24, K2 = 12 ﹤ y = 12x