I. Assemble

Second, the function and its representation

Third, the basic properties of the function

1. Reference Book: Compulsory Mathematics 1 People's Education Edition.

1. Concept: The research objects are collectively called elements, and the sum of elements is called set.

Generally, capital letters A, B, C, ... are used to represent the set, and lowercase letters A, B, C ... are used to represent the elements in the set.

If a is an element of set A, it is said that A belongs to set A, marked as A ∈ A;

If a is not an element of set a, say that a does not belong to set a, and record it as a? Answer.

2. Features: The elements in the set are deterministic, different and out of order.

3. Representation: There are four representations of sets:

(1) natural language method: describe in words, such as all prime numbers in 1-20;

(2) Enumeration: write the elements in the set in braces (for example, a = {0, 1, 2, 3, 4, 5, 6, 7, 8};

(3) Description method: the condition of the set {x|x} is expressed by the * * same characteristics of the elements contained in the set, for example, a = {x ∈ r | x

(4) Graphic method: use number axis or Wayne diagram to represent the set.

4. Classification: Collectibles are divided into the following three categories:

(1) finite set: the set contains a finite number of elements;

(2) Infinite set: the set contains infinite elements;

③ Empty set (? ): The collection does not contain any elements;

There are three relationships between sets:

If set A has n(n≥ 1) elements, then it has 2? A subset, 2? -1 proper subset, 2? -1 nonempty subset, 2? -2 non-empty proper subset.

1. intersection: the set consisting of all elements belonging to set A and set B is called the intersection of A and B, and is marked as A ∩ B. ..

2. Union set: a set consisting of all elements belonging to set A or set B, called the union set of A and B, and marked as A ∪ B. ..

3. Complement set: If a set contains all the elements of the studied problem, it is called a complete set, which is usually recorded as U. For set A, the set composed of all the elements in complete set U that do not belong to set A is called the complement set of set A relative to complete set U, which is called the complement set of set A for short, and is recorded as c? Answer.

1. function concept: let a and b be non-empty number sets. If any number X in set A has a unique number f(x) corresponding to it according to a certain correspondence F, then F: A → B is called a function from set A to set B, and it is denoted as: y=f(x), x \

2. Three elements of a function: domain, range and correspondence. In the concept, X is the independent variable, A is the domain of the function, Y is the function value, the set of Y {f(x)|x∈A} is the range, and F is the corresponding relationship.

3. Same function: Two functions are said to be equal if their domains and corresponding relationships are completely consistent.

4. The concept of interval:

Let a and b be two real numbers, a.

Three common representations of 1. function:

2. The concept of mapping: Let A and B be two nonempty sets. If any element X in set A has a unique element Y corresponding to it according to a certain correspondence F, then the correspondence F: A → B is called the mapping from set A to set B. ..

3. The difference between mapping and function: function is a special mapping, which requires that the elements in two sets must be numbers, while the elements in two sets in the mapping are arbitrary mathematical objects.

1. Maximum: Let the domain of the function y=f(x) be I, and if the real number m satisfies:

(1) For any x∈I, there is f (x) ≤ m;

(2) x 0 ∈ I exists, so f (x 0) = m.

Then, suppose that m is the maximum value of the function y=f(x).

2. Minimum value: Let the domain of the function y=f(x) be I, and if there is a real number m satisfying:

(1) For any x∈I, there is f (x) ≥ m;

(2) x 0 ∈ I exists, so f (x 0) = m.

Then, suppose that m is the minimum value of the function y=f(x).

1. The symmetrical intervals of odd-numbered functions on both sides of the Y axis are the same;

2. Symmetrical intervals of even functions on both sides of Y axis are opposite;

The next part introduces the compulsory basic elementary function (I), which is to be continued. ...