As shown in the figure, points a (m, M + 1) and B (M + 3, m-1) are all on the image of inverse scale function y = KX. (1) find the value of M and K; (2) if M is a point on the x-axis, n is a point on the y-axis, and the quadrilateral with points a, B, m and N as vertices is a parallelogram, try to find the functional expression of straight line Mn

(1) From the meaning of the question, we can see that m (M + 1) = (M + 3) (m-1), the solution is m = 3, (2 points) ∧ a (3,4), B (6,2), ∧ k = 4 × 3 = 12; (3 points) (2) there are two cases, as shown in the figure: ① when m point is on the positive half axis of X axis and N point is on the positive half axis of Y axis, let M1 point coordinate be (x1,0), N1 point coordinate be (0, Y1), ∧ quadrilateral an1m1b be a parallelogram and ∧ line be a line Segment n1m1 can be seen as the result of line segment AB moving 3 units to the left and then 2 units to the down (also can be seen as the result of moving 2 units to the down and then 3 units to the left). Let (1) know that the coordinates of point a are (3,4), the coordinates of point B are (6,2), the coordinates of point N1 are (0,4-2), namely N1 (0,2), and the coordinates of point M1 are (6-3,0), namely M1 (3,0), (4) The function expression of the straight line m1n1 is y = K1X + 2, substituting x = 3 and y = 0, the solution is K1 = − 23, and the function expression of the straight line m1n1 is y = − 23x + 2; (5 points) ② when m point is on the negative half axis of X axis and N point is on the negative half axis of Y axis, let M2 point coordinate be (X2, 0), N2 point coordinate be (0, Y2), ∫ ab ‖ n1m1, ab ‖ m2n2, ab = n1m1, ab = m2n2, ∫ n1m1 ‖ m2n2, n1m1 = m2n2, ∪ The quadrilateral n1m2n2m1 is a parallelogram. The M1 and M2 points are centrosymmetric with the line segments N1 and N2 about the origin O. the coordinates of M2 point are (- 3,0), and the coordinates of N2 point are (0, - 2), (6 points). Let the function expression of the straight line m2n2 be y = k2x-2, and substitute x = - 3 and y = 0. The solution is K2 = - 23. The function expression of the straight line m2n2 is y = - 23x − 2 - 23x + 2 or y = - 23x − 2. (7 points)

Given that the image intersection of the first-order function y = ax + 3 and the inverse scale function y = B / X is ab, its abscissa is 1 and 2 respectively, their analytic expressions are obtained

For y = ax + 3
y=b/x
Substituting x = 1 and x = 2, we get
Y1 = a + 3, Y1 = B, a + 3 = B (1)
Y2 = 2A + 3, y2 = B / 2, then 2A + 3 = B / 2 (2)
Combine (1) (2) together
The solution is A-1 =, B = 2
Substituting analytic expression
y=-x+3,y=2/x

Given that the image of the first-order function y = ax + B intersects with the image of the inverse scale function y = 4x at a (2,2), B (- 1, m), the analytic expression of the first-order function is obtained

Because B (- 1, m) is on y = 4x, so m = - 4, so the coordinates of point B are (- 1, - 4), and the two points of a and B are on the image of a linear function, so − a + B = − 42a + B = 2, the solution is a = 2B = − 2, so the obtained linear function is y = 2x-2

Given that the image of the first-order function y = ax + B is parallel to y = - X and passes through the point Q (1,4), the expression of the first-order function is obtained

A = - 1
So the analytic formula is y = - x + B
Because the straight line passes (1,4)
So 4 = - 1 + B
b=5
So the analytical expression of the line is y = - x + 5

(Zhangzhou, 2013) if an image with inverse scale function y = 8x passes through a point (- 2, m), then the value of M is ()
A. 14B. -14C. -4D. 4

Substituting the point (- 2, m) into the inverse scale function y = 8x, M = 8 − 2 = - 4, so C

Given that y = - (m-2) x exponent is m-square + M-3 is inverse proportional function, then the value of M is

The exponent of the inverse scale function is - 1
So M & sup2; + M-3 = - 1
m²+m-2=0
(m+2)(m-1)=0
m=-2,m=1
The coefficient of inverse scale function is not equal to 0
When m = - 2 and 1, (M & sup2; - 2) is not equal to 0
So m = - 2, M = 1

If the point [4. M] is on the image of inverse scale function y = 8 parts of x [x ≠ 0], then the value of M is?

That is, x = 4, y = M
So m = 8 / 4 = 2

When x = m, y = 2, when x = - 2, y = 3, M = 1

Set
y=k/x
Substituting (- 2, 3) into
k=-6
y=-6/x
Substituting y = 2 into y = - 6 / X
x=m=-3

It is known that the image of the inverse scale function y = m * m / X passes through the point (- 2, - 8), and the image of the inverse scale function y = m / X is in the second and fourth quadrant, and the value of M is obtained

The image of y = m * m / X passes through the point (- 2, - 8),
Yes - 8 = m * m / (- 2)
So m = 4 or - 4
The image with inverse scale function y = m / X is in the second and fourth quadrant
Then M

Known function y = 4 / x ^ 2a-2 is inverse proportion function, request the value of a!
And how to calculate this: 3 = 100 / 5Y

The standard form of inverse scale function is as follows
Y = K / x, where k is a constant,
According to the comparison of the test items, we can see that:
2a-2=1
∴a=3/2