Function I, mapping and function:
The concept of (1) mapping:
(2) One-to-one mapping:
(3) The concept of function:
Second, the three elements of function:
The judgment method of the same function: ① correspondence rule; (2) Domain (two points must exist at the same time)
Solution of resolution function (1):
① definition method (patchwork method): ② substitution method: ③ undetermined coefficient method: ④ assignment method:
(2) The solution of functional domain:
(1) The universe with parameters should be discussed by classification;
(2) For practical problems, after finding the resolution function; We must find its domain, and the domain at this time should be determined according to the actual meaning.
(3) The solution of function value domain:
① Matching method: transform it into a quadratic function and evaluate it by using the characteristics of the quadratic function; Often converted into:;
(2) Reverse solution: the value range used to represent, and then the value range obtained by solving the inequality; Commonly used to solve, such as:
(4) Substitution method: transforming variables into functions of assignable fields and returning to ideas;
⑤ Triangular Bounded Method: Transform it into a function containing only sine and cosine, and use the boundedness of trigonometric function to find the domain;
⑥ Basic inequality methods: transformation and modeling, such as: using the average inequality formula to find the domain;
⑦ Monotonicity method: The function is monotonous, and the domain can be evaluated according to the monotonicity of the function.
⑧ Number-shape combination: According to the geometric figure of the function, the domain is found by the method of number-shape combination.
2. People's Education Edition requires three knowledge points in senior three mathematics.
Chapter 1: Trigonometric function. The exam must be answered. Some properties of inductive formulas and basic trigonometric function images can be remembered as long as they can draw pictures. The difficulty lies in the amplitude, frequency, period, phase and initial phase of trigonometric function, and the calculation of the values and periods of A and B according to the maximum value, as well as the changes of images and properties when constants change. This knowledge point has more contents and takes more time. First of all, you should remember. Secondly, you should do more exercises. As long as you can do it in a down-to-earth manner, it is not difficult to master it. After all,
Chapter 2: Plane vector. Personally, I think this chapter is more difficult, and it is also the chapter I have the worst grasp. The operational properties of vectors and the rules of triangles and parallelograms are not difficult, as long as you remember the vectors with the same starting point when calculating. The mathematical expressions of vector * * * straight line and vertical line are often used in calculation. * * * Straight line theorem, basic theorem of vector and formula of quantity product. The difficulty lies in the formula of vernal equinox coordinates. First, we must remember accurately. General vectors do not appear alone in the examination process, but often appear as problem-solving tools. When using vectors, we must first find the appropriate vector. Personally, I think this is more difficult and often wrong. Students with the same situation suggest reading more pictures.
Chapter 3: Triangular identity transformation. There are many formulas in this chapter. There are also formulas of difference times and half angles, which are all used, so be sure to remember them. Because the amount is relatively large and difficult to remember, it is recommended to write it on paper and stick it on the table, and read it every day. Moreover, trigonometric function transformation has certain rules, which can be combined to remember when remembering. Besides, practice more. We should look for the law of transformation from more practice, such as simplification and so on. This chapter is also required in the exam, so we must focus on it.