Given that the ordinate of the intersection of the image of a certain function and the Y axis is - 1, and when x = 3, y = - 4, what is the expression of this function?

Given that the ordinate of the intersection of the image of a certain function and the Y axis is - 1, and when x = 3, y = - 4, what is the expression of this function?

Let y = kx-1
When x = 3, y = - 4
-4=3k-1
-3=3k
k=-1
y=-x-1

Given that the coordinates of the intersection of the image of a certain function and the x-axis and y-axis are (- 2,0) (0,4), the expression of this function is a detailed solution process
The knowledge point is the primary function of mathematics in Volume 1 of grade 2 of junior high school

By taking (- 2,0) (0,4) into y = KX + B, we get
-2k+b=0
b=4
The solution is k = 2, B = 4
y=2x+4

Given the image of the first-order function through (0.1), (- 1, - 3), find the expression of the first-order function, and find the intersection of the image and X axis

Let this function be y = KX + B
When x = 0, y = 1 (0,1) and x = - 1, y = - 3 (- 1, - 3)
1 = 0 * k + b
-3 = -1 * k + b
The solution is k = 4, B = 1
Then the function is y = 4x + 1
The intersection of image and X axis y = 0
0=4x+1
x=-1/4
Intersection (- 1 / 4,0)

If the ordinate of the intersection point a between the image of the first-order function and the y-axis is - 2, and the area of the triangle surrounded by the two axes is 1, then the expression of the first-order function is_

Let the expression be y = KX + B
Substituting point a (0, - 2) into
-2=b
y=kx-2
When x = 0, y = - 2
When y = 0, x = 2 / K
Area = | - 2 | - 2 / K | - 2 = 1
The solution is k = 1 or K = - 1
So y = X-2 or y = - X-2

Given that a positive scale function image passes through a point (- 2,4), the expression of the positive scale function is__________ .

Let y = KX,
(- 2,4), k = - 2,
So y = - 2x

It is known that the image of positive scale function y = MX and linear function y = NX + B intersect at point a (8,6), the image of linear function intersects with X axis at point B, and ob = 3 / 5oa
Find the analytic expressions of these two functions
If n is a linear function, y = NX + B is a point on the image, and s triangle OBN: s triangle AON = 1:2, the analytic expression of line on is obtained

M = Y / x = 6 / 8 = 3 / 4 analytical formula of scale function: y = 3 / 4 * x has the problem meaning to know B (- B / N, 0), and OA = 10, so ob = 6, that is - B / N = 6 ------ (1) plus a in the graph of first-order function, so 6 = 8N + B ------ (2) two equations can be obtained: n = 3, B = - 18, the analytical formula of first-order function is: y = 3x-18s

It is known that the image of positive scale function y = MX and linear function y = NX + B intersects at point a (8,6), the image of linear function intersects at point B, and ob = 3 / 5oa
I find out the analytic expressions of the two functions as follows:
Positive scale function: y = 3 / 4x
Linear function: y = 3x-18 or y = 3 / 7X + 18 / 7
Now, if n is a linear function, y = NX + B is a point on the image, and s triangle OBN: s triangle AON = 1:2, find the analytic expression of line on

OA=10
OB=3/5OA=6
B (- 6,0) or (6,0)
Positive scale function: y = 3 / 4x
Linear function: y = 3x-18 or y = 3 / 7X + 18 / 7
There are four such n points
1: On the line y = 3x-18, between AB, Nb: Na = 1:2; n [6 + 2 / 3,0 + 6 / 3] = [20 / 3,2]
2: On the line y = 3x-18, on the extension line AB, ab = BN; n [4, - 6]
3: On the line y = 3 / 7X + 18 / 7, between AB, Nb: Na = 1:2; n [- 6 + 14 / 3, (0 + 6) / 3] = [- 4 / 3,2]
4: On the line y = 3 / 7X + 18 / 7, ab = BN; n [[- 20, - 6]
The corresponding on expression is as follows:
1:y=3x/10
2:y=-3x/2
3:y=-3x/2
4:y=3x/10
There are two overlaps, actually two:
1:y=3x/10
2:y=-3x/2

The ordinate of the intersection point between the image with positive scale function y = x and the image with inverse scale function y = K / X is 2
(1) The value of inverse proportional function y when x = - 3;
(2) When - 3 ∠ x ∠ - 1, the value range of inverse proportional function y is obtained
PS: there are points plus

From y = x, the coordinates of intersection (2,2) are obtained, so k = 4
(1) When x = - 3, the inverse proportional function y = 4 / (- 3) = - 4 / 3
(2) When x

An intersection point between the image of positive scale function y = (m-2) x and the image of inverse scale function y = (M + 1) / X is a, and the abscissa of point a is 2

The ordinates of intersections are equal
So when x = 2, the two Y's are equal
SO 2 (m-2) = (M + 1) / 2
4m-8=m+1
m=3
So the inverse scale function is y = 4 / X

In the same rectangular coordinate system, the image of an inverse scale function and the image of a positive scale function intersect at two points a and B, and point a is in the second quadrant
If the abscissa of point a is - 3, ad is perpendicular to the X axis, and the perpendicular foot is D, the area of triangle AOD is known to be 4. (1) write out the relationship of the inverse scale function. (2) find the coordinates of point B. (3) if the coordinates of point C are (6,0), find the area of triangle ABC

(1) Let the positive scale function y = KX, the inverse scale function y = A / x, the area of triangle AOD be 4, the abscissa of point a is - 3, and point a is in the second quadrant, so the coordinates of point a (- 3,8 / 3) and point a are on two functions, so 8 / 3 = - 3k, 8 / 3 = A / (- 3) k = - 8 / 9, a = - 8, the expression of inverse scale function is y = - 8 / x, and the positive scale is y = - 8 / 9 * x (2) B