MindMap Gallery The concept and properties of functions
This is a mind map about the concept and properties of functions. It summarizes and organizes knowledge points and covers all core content, which is very convenient for everyone to learn. Suitable for exam review and preview, improving learning efficiency. Hurry up and collect and study together!
Edited at 2025-01-05 08:45:18Rumi: 10 dimensions of spiritual awakening. When you stop looking for yourself, you will find the entire universe because what you are looking for is also looking for you. Anything you do persevere every day can open a door to the depths of your spirit. In silence, I slipped into the secret realm, and I enjoyed everything to observe the magic around me, and didn't make any noise. Why do you like to crawl when you are born with wings? The soul has its own ears and can hear things that the mind cannot understand. Seek inward for the answer to everything, everything in the universe is in you. Lovers do not end up meeting somewhere, and there is no parting in this world. A wound is where light enters your heart.
Chronic heart failure is not just a problem of the speed of heart rate! It is caused by the decrease in myocardial contraction and diastolic function, which leads to insufficient cardiac output, which in turn causes congestion in the pulmonary circulation and congestion in the systemic circulation. From causes, inducement to compensation mechanisms, the pathophysiological processes of heart failure are complex and diverse. By controlling edema, reducing the heart's front and afterload, improving cardiac comfort function, and preventing and treating basic causes, we can effectively respond to this challenge. Only by understanding the mechanisms and clinical manifestations of heart failure and mastering prevention and treatment strategies can we better protect heart health.
Ischemia-reperfusion injury is a phenomenon that cellular function and metabolic disorders and structural damage will worsen after organs or tissues restore blood supply. Its main mechanisms include increased free radical generation, calcium overload, and the role of microvascular and leukocytes. The heart and brain are common damaged organs, manifested as changes in myocardial metabolism and ultrastructural changes, decreased cardiac function, etc. Prevention and control measures include removing free radicals, reducing calcium overload, improving metabolism and controlling reperfusion conditions, such as low sodium, low temperature, low pressure, etc. Understanding these mechanisms can help develop effective treatment options and alleviate ischemic injury.
Rumi: 10 dimensions of spiritual awakening. When you stop looking for yourself, you will find the entire universe because what you are looking for is also looking for you. Anything you do persevere every day can open a door to the depths of your spirit. In silence, I slipped into the secret realm, and I enjoyed everything to observe the magic around me, and didn't make any noise. Why do you like to crawl when you are born with wings? The soul has its own ears and can hear things that the mind cannot understand. Seek inward for the answer to everything, everything in the universe is in you. Lovers do not end up meeting somewhere, and there is no parting in this world. A wound is where light enters your heart.
Chronic heart failure is not just a problem of the speed of heart rate! It is caused by the decrease in myocardial contraction and diastolic function, which leads to insufficient cardiac output, which in turn causes congestion in the pulmonary circulation and congestion in the systemic circulation. From causes, inducement to compensation mechanisms, the pathophysiological processes of heart failure are complex and diverse. By controlling edema, reducing the heart's front and afterload, improving cardiac comfort function, and preventing and treating basic causes, we can effectively respond to this challenge. Only by understanding the mechanisms and clinical manifestations of heart failure and mastering prevention and treatment strategies can we better protect heart health.
Ischemia-reperfusion injury is a phenomenon that cellular function and metabolic disorders and structural damage will worsen after organs or tissues restore blood supply. Its main mechanisms include increased free radical generation, calcium overload, and the role of microvascular and leukocytes. The heart and brain are common damaged organs, manifested as changes in myocardial metabolism and ultrastructural changes, decreased cardiac function, etc. Prevention and control measures include removing free radicals, reducing calcium overload, improving metabolism and controlling reperfusion conditions, such as low sodium, low temperature, low pressure, etc. Understanding these mechanisms can help develop effective treatment options and alleviate ischemic injury.
The concept and properties of functions
Function definition
definition
Each input corresponds to a unique output
Definition of the domain
A collection of function input values
range
A collection of function output values
Corresponding rules
Conversion rules between input and output
Function representation method
Analytical
Define functional relationships with mathematical expressions
image
Drawing function graphs in coordinate system
sheet
Table of values that list input and output corresponding to
Text description
Describe functional relationships in natural language
Properties of functions
Monotony
Function value increases or decreases as input value increases
Periodicity
Function values appear repeatedly in a certain period
Parity
Function image symmetric about origin or y-axis
Continuity
Function image has no interruption points
Special function type
Linear functions
A function, the image is a straight line
Quadratic functions
Quadratic polynomial function, image is parabola
Exponential Function
Functions of fixed base and exponential change
Logarithmic function
Inverse operation of exponential functions
Trigonometric function
Periodic functions related to angles
Function operation
Addition, subtraction, multiplication and division
Four operations between functions
Compound functions
The output of one function becomes the input of another function
Inverse function
Inverse operation of the original function, input and output interchange
Application of functions
Mathematical Modeling
Use functions to describe real-world problems
Engineering calculation
Functions are used to solve engineering problems
Scientific research
Application of functions in scientific experimental data analysis
Economic Analysis
Application of functions in economic models
Power function
definition
General form
f(x) = x^n
n is a real number
The properties of the index n
Positive integer exponent
Function image rise
Negative integer exponent
Function image drop
Fraction index
Include root number
Image Features
n is a positive integer
Images pass through the origin
Symmetry to the y-axis
n is a negative integer
The image does not pass through the origin
The asymptomatic line is the x-axis
n is the fraction
The image asymptomatic line is the y-axis
nature
Monotony
n is the timing monotonically increasing
When n is negative, monotonically decreasing
Parity
When n is an odd number, it is an odd function
When n is an even number, it is an even function
Asymptomatic
x-axis or y-axis
Special power function
Square function
f(x) = x^2
Cube Function
f(x) = x^3
Square Root Function
f(x) = x^(1/2)
Countdown function
f(x) = x^(-1)