Properties of graph of first order function Y = ax + B when a is greater than 0, in which quadrant is the image? When a is less than 0, in which quadrant is the image? When B is greater than 0, in which quadrant is the image? When B is less than 0, in which quadrant is the image?

Properties of graph of first order function Y = ax + B when a is greater than 0, in which quadrant is the image? When a is less than 0, in which quadrant is the image? When B is greater than 0, in which quadrant is the image? When B is less than 0, in which quadrant is the image?

It is related to a and B
a> 0 b > 0 image passing through 123 quadrants
a>0 b
Given that set a = {x | x > 1}, set B = {x | m ≤ x ≤ m + 3}, if B is contained in a, then the value range of real number m is?
It is easy to know that B is not an empty set, so as long as M is greater than 1, B can be contained in a
Draw a real axis and you'll see
Since B is contained in a, the left end of B must be on the right side of 1
So m > 1
What are the images and properties of positive scale function?
The image of positive scale function is a straight line passing through the origin. When k is greater than 0, the straight line extends upward infinitely. When k is equal to 0, it coincides with the X axis. When k is less than 0, the straight line extends downward infinitely
The known set a = {x | 0 ≤ x-m ≤ 3}, B = {x | x}
(1)
A={x| 0≤x-m≤3 },B={x| x
m≥0 and 3+m ≤ 3
m≥0 and m ≤0
=> m=0 #
(2)
A∪B=B => A is subset of B
3+m< 0 or m>3
m< -3 or m > 3 #
How to parallel the images of two first order functions
What are the characteristics of the expressions of two linear functions
The K value is the same
B value is different
When f (x) - G (x) is a constant, the images of F and G are parallel
Y = KX + B when the k values of two linear functions are equal, the images of the two functions are parallel
Let the general expression be
y=kx+b
When k is equal, it is parallel
B is not equal
Given the nonempty set a = {x | M0}, if a ∪ B = B, then the value range of real number m is
A={x|m0}
∵A∪B=B
A is contained in B, i.e
M > 0, and a is a nonempty set
∴m＜3
∴m∈（0,3）
If the image of a linear function passes through the point (- 2,2) and intersects with the positive scale function y = 5x at the point (a, 5), the analytic expression of the linear function is obtained
Let the analytic formula of a function be y = KX + B
∵ the image of a linear function intersects with the positive scale function y = 5x at point (a, 5),
The point (a, 5) is also on the positive scale function
5*a=5
A = 1
The point (- 2,2) and point (1,5) are substituted into the analytic expression of the first-order function
2=(-2)*k + b
5=1*k + b
The solution is: k = 1, B = 4
The analytic formula of a function is y = x + 4
Through the point (- 2,2), (1,5), we know that y = x + 4
Substituting x = a, y = 5 into y = 5x leads to
5=5a
A=1
Let the analytic expression of a function be y = KX + B
Substitute x = - 2, y = 2, x = 1, y = 5 into the above formula
(here is a system of linear equations of two variables)
The solution is k = B=
So the analytic expression is_____ .
For reference
∵ y = 5x over point (a, 5)
∴a=1
Let y = ax + B pass through points (- 2,2) and (1,5)
∴y=x+4
Let the analytic expression of the function be y = KX + B, because the image is over (- 2,2)
The formula 2 = - 2K + B1 is replaced by (a, 5) because it intersects with the positive proportion function y = 5x to get a = 1
Substituting y = KX + B, we get 5 = K + B and K = 1, B = 4
So the analytic expression of the function is y = x + 4
Let u = {0,1,2,3,4,5}, M = {0,3,5}, n = {1,4,5}, then m ∩ (Cun} is equal to
Write more clearly
Set u = {0,1,2,3,4,5}, set M = {0,3,5}, n = {1,4,5}, then Cun = {0,2,3}, then m ∩ (Cun} = {0,3}
CuN={0,2,3}, M={0,3,5}, M∩（CuN)={0,3}
Take a close look at the textbook how to say Union, intersection and complement these basic operations, more experience
Cun = {0, 2, 3}; the final result is {0, 3}
What is the coordinate of a symmetry center of the image of the function y = sin (3x - π / 4)?
（π/12,0）
The center of symmetry of sine function is (π / 2 + K π, 0)
So the other 3x - π / 4 = π / 2 + K π is X
For two sets AB, define A-B = {x ∈ a, and do not belong to B}, then a - (a-b)=
The answer is a ∩ B (intersection of a and b)
It is also possible to use logical methods without graphics
because
A - B = {x | x ∈ a, and X does not belong to B}
therefore
A - (a-b) = {x | x ∈ a, and X does not belong to (a-b)}
According to the definition of a - (a-b), X does not belong to (a-b), so according to the definition of (a-b), X does not belong to a, or X ∈ B
From the definition of a - (a - b), we know that x ∈ a
To sum up
A - (a - b) = {x | x ∈ a, and (x does not belong to a, or X ∈ b)}
={x | (x ∈ a, and X does not belong to a) or (x ∈ a, and X ∈ b)}
={x | (contradiction) or (x ∈ a, and X ∈ b)}
={x | x ∈ a, and X ∈ B}
= A∩B.
Note: the error of yzngb is that the negation of "x belongs to a, and does not belong to B" is "X does not belong to a, and X does not belong to B", which is wrong. In fact, it should be "X does not belong to a, or X does not belong to B". If you learn a little mathematical logic, you will understand these logical operations
empty set
A - (a-b) description
1. X belongs to a
2. X does not belong to A-B, that is, it does not belong to {x ∈ a, and does not belong to B}, that is = {x ∈ B, and does not belong to a}