The inverse scale function y = K / X and the first-order function y = - x + 8 are known (1) If the images of the first-order function and the inverse scale function intersect at (4, m), the values of M and K are obtained (2) When k satisfies what condition, the images of these two functions have two different intersections? (3) Let the two intersection points in (2) be a and B. try to judge whether ∠ AOB is an acute angle or an obtuse angle?

The inverse scale function y = K / X and the first-order function y = - x + 8 are known (1) If the images of the first-order function and the inverse scale function intersect at (4, m), the values of M and K are obtained (2) When k satisfies what condition, the images of these two functions have two different intersections? (3) Let the two intersection points in (2) be a and B. try to judge whether ∠ AOB is an acute angle or an obtuse angle?

Substitute x = 4 for y = - x + 8 to get m = 4
Substituting x = 4 into y = K / X yields k = 16
y=4
k

The inverse proportional function y = K / X (K ≠ 0) and the first-order function y = - x + 8 are known
1. If the images of the first-order function and the inverse scale function intersect at point (4, m), find m and K
2. When k satisfies what conditions, the two function images have two different intersections
3. Let two intersections in 2 be points a and B, and try to judge whether ∠ AOB is an acute angle or an obtuse angle

1. Take x = 4, y = - x + 8, y = - 4 + 8, y = 4, so m = 4, take (4,4) into y = K / x, k = 16
2. K is greater than 16
3. Sharp angle

It is known that the image of inverse scale function y = KX and primary function y = MX + n pass through the point (- 3,1), and when x = 12, the function values of these two functions are equal. The analytic expressions of these two functions are obtained

∵ the images of inverse scale function y = KX and primary function y = MX + n all pass through the points (- 3, 1), ∵ k = - 3, 1 = - 3M + n ①, and ∵ when x = 12, the function values of the two functions are equal, ∵ 3 △ 12 = 12m + n ②, and the solution of simultaneous ① and ② is m = - 2, n = - 5, ∵ y = - 2x-5

On the image of the inverse scale function y = - K / x, we observe that when the value of X decreases from 4 to 2, the value of Y decreases by 3. You can find out the function from this information

When x = 4, y = - K / 4,
When k = 2, y = - K / 2,
Because the value of Y is reduced by 3,
So (- K / 4) - (- K / 2) = 3
The solution is k = 12,
The function is y = - 12 / X

If the image of inverse scale function y = K / X passes through point (2, - 1), then the value of K is_____
2. For the four points a (1,2), B (2,1), C (- 1, - 2) and D (- 2, - 1) in the plane rectangular coordinate system, there is ()
A. 1 point B.2 points C.3 points D.4 points
3. Draw the graph of function y = 6 / X
(1) To trace the grid points on the image in the first quadrant, X should take the following values:_____
(2) In order to draw an image closer to two adjacent points, so that the image can be drawn more accurately, please write down the coordinates of the two points you intend to add in the first quadrant_____

1、-2
2、D
3、1、2、3、6
x=4、5

As shown in the figure, a straight line intersects with the image of inverse scale function y = K / X at two points a (1,4) B (4, n), intersects with X axis at point D, AC ⊥ X axis, and the perpendicular foot is C
(1) As shown in figure a, ① find the analytic expression of inverse scale function; ② find the value of N and the coordinate of D point;
(2) As shown in Figure B, if point e moves on line ad, connect CE, make ∠ CEF = 45 ° and EF intersect AC at point F
① Try to explain △ CDE ∽ EAF;
② When △ ECF is an isosceles triangle, the coordinates of F point are written directly

(1) Let ∵ point a (1,4) be on the image of inverse scale function ∵ k = 4, that is, the relation of inverse scale function is y = 4x; let ∵ point B (4, n) be on the image of inverse scale function ∵ n = 1. Let the analytic formula of the first-order function be y = MX + B ∵ point a (1,4) and B (4,1) be on the image of the first-order function y = MX + B ∵ m + B = 4m + B = 1

As shown in the figure, the image of the first-order function y = x + 1 and the inverse scale function y = K / X intersects at point a (2,3), and the analytic expression of the inverse scale function is obtained

∵ point a (2,3) is on the function y = K / X,
∴3=k/2,
k=6
The analytic expression of inverse scale function is y = 6 / X
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For the image of inverse scale function y = k − 3x, when x > 0, y increases with the increase of X, then the value range of K is ()
A. k＜3B. k≤3C. k＞3D. k≥3

∵ when x ＞ 0, y increases with the increase of X. the image of the function must be in the fourth quadrant, ∵ K-3 ＜ 0, ∵ K ＜ 3

If the image of the known inverse scale function passes through the point (2, - 2), then y is obtained

Y = - 4 / X is an increasing function (the larger x is, the larger y is)
Discussion according to the situation:
（1）x 0
To sum up, the value range of X is: x > 0 or x < - 2

In the following example function, y is a linear function of X, and a, y = - 3 plus 5, B, y = - 3x square, C, y = 1 / x, D, y = - 2x

D