MindMap Gallery Linear function - junior high school mathematics
Linear function - junior high school mathematics, mainly includes the image of linear function, The application of primary functions, functions and their representation, etc.
Edited at 2024-02-11 16:24:23Avatar 3 centers on the Sully family, showcasing the internal rift caused by the sacrifice of their eldest son, and their alliance with other tribes on Pandora against the external conflict of the Ashbringers, who adhere to the philosophy of fire and are allied with humans. It explores the grand themes of family, faith, and survival.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
Avatar 3 centers on the Sully family, showcasing the internal rift caused by the sacrifice of their eldest son, and their alliance with other tribes on Pandora against the external conflict of the Ashbringers, who adhere to the philosophy of fire and are allied with humans. It explores the grand themes of family, faith, and survival.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
Linear function
Function and its representation
Constants and variables
Constant: A quantity that has a fixed value during a certain change process
Variable: A quantity whose value will change during a certain change process
Judgment criteria: See whether the value of the quantity changes during the change process
y=4x2
Variables - y, x
Constant - 4, 2
function
Definition: Generally, if the variable y changes with the variable x, and for each value of x, y has a unique value corresponding to it, then y is said to be a function of x, recorded as y=f(x), At this time, x is called the independent variable and y is called the dependent variable.
The value range of function arguments
Integer type (y=4x 1)——all real numbers
Fractional type (y=A/B)——x≠0
Radical type (y=√A)——A≠0
Zero power type (y=Aº)——a≠0
Representation method of function
Analytical method is convenient List method clear Image method intuitive
image
Steps to draw function graph
list
Draw points
Connect
Linear function
linear function and proportional function
Proportional function A function of the form y=kx (k is a constant, k is not equal to zero) is called a proportional function
The proportional function is a special linear function
A function of the form y=kx b(k, b is a constant, k is not equal to zero) is called a linear function.
image pan
Adding up and subtracting at the end
Left plus right minus within brackets
image parallel
K values are the same
Image intersection
By making the dependent variables of the two expressions the same, the intersection coordinates can be obtained
vertical
k1k2=-1
Application of one-time function
Quadratic equations and linear functions
linear equation of one variable → linear function ax b=0→y=ax b
Angle of number: When y=0, the value of x
Image angle: the abscissa of the intersection of straight line y=ax b and the axis
Solution of the equation
Univariate linear inequalities and linear functions
linear inequality of one variable → linear function ax b>0→Above the X-axis ax b<0→below the X-axis
Determine the value range of y through the abscissa coordinate of the intersection of the image and the x-axis
System of linear equations of two variables and linear function (intersection problem)
The intersection point of the two lines is the solution set
piecewise function
Solve the analytical expressions of different segments using the method of undetermined coefficients
The x values of different segments have different value ranges
plan selection
Use the properties of the k value to determine the final value
The image of a linear function
The image and properties of the proportional function
Shape: The graph of the proportional function y=kx is a straight line passing through the origin
Two-point method: Generally choose (0, 0) (1, k) two points to draw the picture
When k>0, the straight line y=kx passes through one or three quadrants, and y increases with the increase of x.
When k<0, the straight line y=kx passes through the second and fourth quadrants, and y decreases as x increases.
The larger (smaller) the value of |k|, the steeper (slower) the image is.
The image and properties of a linear function
Shape: a straight line
Two-point method: General selection (-b/k, 0) (0, b)
When k>0, b>0, the straight line y=kx b passes through the first, second, and third quadrants, and y increases with the increase of x.
When k>0, b<0, the straight line y=kx b passes through the first, third, and fourth quadrants, and y increases with the increase of x.
When k<0, b>0, the straight line y=kx b passes through the first, second, and fourth quadrants, and y decreases as x increases.
When k<0, b<0, the straight line y=kx b passes through the second, third, and fourth quadrants, and y decreases as x increases.
Determining a linear function expression using the method of undetermined coefficients
Determining a linear function expression using the method of undetermined coefficients
"Suppose" establish the general formula of a linear function "Substitute" into a set of corresponding values "Solution" solve this system of equations to find the values of k and b "Substitute" k and b to get the analytical formula of the linear function