The concept of 1. function: First of all, we must clarify the concept of function, including the basic elements such as definition domain, range, correspondence law, and the properties of function such as monotonicity, parity, periodicity and symmetry.
2. Representation methods of functions: The representation methods of functions include list method, analytical formula method and image method. Different representation methods have their own advantages and disadvantages, so it is necessary to choose the appropriate representation method according to the specific situation.
3. Properties of functions: The properties of functions include monotonicity, parity, periodicity, symmetry, etc. These properties are the basis of function teaching and an important aspect of function application.
4. Application of functions: Functions are widely used, including series, inequalities and equations. These applications can help students better understand the concept and nature of functions, and also cultivate their mathematical thinking and application ability.
5. Function modeling and optimization: Function modeling and optimization is the difficulty and focus of function teaching, which needs to be explained and practiced in combination with specific problems to help students master the methods of function modeling and optimization.
The application of the function of secondary vocational education;
1, function and equation: understand the relationship between function and equation, and master how to use the knowledge of function to solve equation problems, such as solving the roots of a quadratic equation with one variable.
2. Function and inequality: understand the relationship between function and inequality, and master how to use the knowledge of function to solve inequality problems, such as solving the solution set of linear inequality.
3. Function and sequence: Understand the relationship between function and sequence, and master how to use the knowledge of function to solve sequence problems, such as solving arithmetic progression's general formula.
4. Function and geometry: Understand the relationship between function and geometry, and master how to use the knowledge of function to solve geometric problems, such as solving the tangent equation of a circle.
5. Function and optimization: understand the relationship between function and optimization, and master how to use the knowledge of function to solve optimization problems, such as solving the maximum and minimum values.