Can you teach me how to draw the image of y = 4x function?

Can you teach me how to draw the image of y = 4x function?

Draw a point (0,0), then a point (2,8) on the rectangular coordinate system, and then draw a straight line through the two points

Function y=________ The image of X is a straight line passing through the origin and (- 1,2)____

y=kx
2=-k
k=-2
Then the function y=__ y=-2x______ The image of X is a straight line passing through the origin and (- 1,2)__ Decrease__

Image properties of function y = x ^ 3
As the title!
What I want to know is:
The shape of the image
Points passed

1. Monotonic increase
2. Odd function
3. Derivable on R
4. Convex function on (- infinity, 0) and concave function on (0, + infinity)
5.…… What else? & nbsp;
The graph of passing (0,0), (1,1), (- 1, - 1) is as follows:

Find the check function y = ax + B / X (a > 0, B

Taking a = 1, B = - 1, we get the following result:
So this is no longer a tick shape

If the point [1,2] is on the image of the function y = ax + B and y = X-B / a at the same time, then the point [a, b] is

Substituting points (1,2) into two functions respectively, we can get the system of linear equations with one variable about a and B, and then we can get the solution
According to the meaning of the title, we can get 2 = a + B
2=1-b/a
The solution is a = - 1
b=3
[a, b] is (- 1,3)

The image and properties of y = ax + B / X
Understanding the nature of images

Students are too far away, do not remember, the nature of the image should refer to the kind of parity symmetry
This image is symmetric about y = - X or y = X

It is known that the image of inverse scale function y = (2m + 5m) / X intersects with the first-order function y = MX + 3N at points (1, - 2),

Point (1, - 2), substituting y = (2m + 5m) / x = 7m / X
-2=7m/1
m=-2/7
Inverse scale function y = - 2 / X
y=mx+3n
Is y = - 2x / 7 + 3N, point (1, - 2), substituting
-2=-2/7+3n
3n=-12/7
n=-4/7
Linear function y = - 2x / 7-12 / 7

It is known that the image of the first-order function y = MX + N and the inverse scale function y = 3N-M / X intersects at the point (2,4). Try to find the expression of these two functions

Bring (2,4) in respectively
Then 2m + n = 4, - M / 2 + 3N = 4
The solution is m = 16 / 13, n = 20 / 13
So y = 16 / 13X + 20 / 13
y=60/13-16/13x

The images of the first-order function y = MX + 3N and the inverse scale function Y2 / X are all calculated by (- 1, - 2) ① to find the coordinates of another intersection point of M and N ②

If the two intersection points of the first-order function and the inverse proportion function are symmetrical about the origin, then the coordinates of the other intersection point are (1,2), and the two coordinates are substituted into the expression of the first-order function to obtain M = 2, n = 0

It is known that the image of the first-order function y = MX + N and the inverse scale function y = 3N-M / X intersects at the point (1 / 2,2)
The coordinates of the other intersection of the hyperbola are (,)

By substituting x = 1 / 2, y = 2 into y = MX + N and y = (3N-M) / x, we can get the equations of M and N: 1 / 2m + n = 2 (1) (3N-M) / (1 / 2) = 2 (2) to simplify (1) to simplify (2) to simplify (2) to simplify (2) to simplify (2) to obtain: 3N-M = 1 (4) (3) + (4) to obtain: 5N = 5N = 1 to substitute (3) to obtain: M + 2 = 4m = 2. Therefore, the analytic formula of the first-order function is y =