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Anonymous users2024-02-07To learn functions, we should focus on solving four problems: accurately and profoundly understand the relevant concepts of functions; Reveal and recognize the intrinsic relationship between functions and other mathematical knowledge; grasp the characteristics and methods of the combination of numbers and shapes; Understand the essence of functional thinking and strengthen the sense of application.
1) Accurate and deep understanding of the relevant concepts of functions.
Concepts are the foundation of mathematics, and functions are one of the most important concepts in mathematics, and the concept of functions runs through algebra in middle school. Numbers, formulas, equations, functions, permutations and combinations, sequence limits, etc., are function-centered algebras. In the past ten years, the main line of functions and their properties has always run through the questions of the college entrance examination.
2) Reveal and recognize the intrinsic relationship between functions and other mathematical knowledge. Function is the study of variables and interrelated mathematical concepts, is the basis of variable mathematics, using the function perspective can be used to deal with formulas, equations, inequalities, sequences, curves and equations from a higher perspective. In the use of functions and equations for thinking, dynamic and static, variable and constant are so vividly dialectically unified, functional thinking is actually a special form of dialectical thinking.
The so-called functional view is essentially to consider the problem in a dynamic context. The questions in the college entrance examination involve five aspects: (1) function problems in the original sense; (2) Equations and inequalities are solved as functional properties; (3) The number series has become a hot spot in the college entrance examination as a special function; (4) auxiliary function method; (5) Sets and mappings, which appear in the test questions as basic languages and tools.
3) Grasp the characteristics and methods of the combination of numbers and shapes.
The geometric characteristics of the function image are closely combined with the quantitative characteristics of the function properties, which effectively reveals the basic properties of various functions and definition domains, value domains, monotonicity, parity, periodicity, etc., and embodies the characteristics and methods of the combination of numbers and shapes.
4) Understand the essence of functional thinking and strengthen the awareness of application.
The essence of the idea of function is to put forward mathematical objects from the viewpoint of connection and change, abstract quantitative features, establish functional relations, and solve problems. Throughout the college entrance examination questions in recent years, the examination of functional thinking methods, especially application questions, has increased, so it is necessary to understand the essence of functional thinking and strengthen the application awareness.
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Anonymous users2024-02-06Definition of function in junior high school: There are two variables in a certain change process, such as x, y, when x changes, y has a unique value corresponding to it, then x is called the independent variable, and y is called the function of x, referred to as the function y
1.The independent variable x can take many values and can be varied, not fixed.
2.The value of the function, that is, the value of y, changes with the change of x, and y changes because of the change of x, so x is called an independent variable, and no matter how x changes, the value of y can be calculated by some law to calculate the only result.
For example: y = 2x +1 is a function called : y is a function of x, x is an independent variable, and the function is yy=1 x is also a function, but x≠0
s= r This is a function of s is r.
c= 2 r, this is a function of c is r.
In general: the letter to the left of the equal sign is a function, and the letter to the right of the equal sign is an independent variable.
In junior high school, there are three basic functions: the primary function, the inverse proportional function and the quadratic function.
For example: incrementality, quadrants and axes of intersection, etc.
Primary function : y = kx + b
Inverse proportional function: y = k x
Combine images to figure out the geometric meaning of k and b, and that's pretty much it.
Quadratic functions are the hardest, but remember the mantra: one bite of the two axes and three vertices after the intersection and then add or subtract.
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Anonymous users2024-02-05Definition of function in junior high school: There are two variables in a certain change process, such as x, y, when x changes, y has a unique value corresponding to it, then x is called the independent variable, and y is called the function of x, referred to as the function y
1.The independent variable x can take many values and can be varied, not fixed.
2.The value of the function, that is, the value of y, changes with the change of x, and y changes because of the change of x, so x is called an independent variable, and no matter how x changes, the value of y can be calculated by some law to calculate the only result.
For example: y = 2x +1 is a function called : y is a function of x, x is an independent variable, and the function is y
y=1 x is also a function, but x≠0
s= r This is a function of s is r.
c= 2 r, this is a function of c is r.
In general: the letter to the left of the equal sign is a function, and the letter to the right of the equal sign is an independent variable.
In junior high school, there are three basic functions: the primary function, the inverse proportional function and the quadratic function.
For example: incrementality, quadrants and axes of intersection, etc.
Primary function : y = kx + b
Inverse proportional function: y = k x
Combine images to figure out the geometric meaning of k and b, and that's pretty much it.
Quadratic functions are the hardest, but remember the mantra: one bite of the two axes and three vertices after the intersection and then add or subtract.
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Anonymous users2024-02-04It's important to think about the logical order of functions, and with proper practice.
For the teacher to understand and memorize what he said in class, it is important to have an appropriate amount of [review] and [do questions] after class, and it is very important to write the logical order in the multi-thinking function, and then it is necessary to have appropriate exercises. Junior high school!? High school.
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