What is the element?
Pay attention to the set problem with the help of number axis and venn diagram.
An empty set is a subset of all sets and the proper subset of all non-empty sets.
3. Please note the following attributes:
(3) De Morgan's Law:
4. Can we solve the problem with the idea of complement set? (Exclusion method, indirect method)
The value range of.
6. What are the four forms of propositions and their relationships?
A proposition with reciprocal negation is an equivalent proposition. )
Both the original proposition and the negative proposition are true and false; Whether it is an inverse proposition or not, a proposition is the same as true or false.
7. Do you know the concept of mapping? Mapping F: A → B, have you noticed the arbitrariness of elements in A and the uniqueness of corresponding elements in B? What kind of correspondence can constitute a mapping?
(one-to-one, many-to-one, allowing the elements in B to have no original image. )
8. What are the three elements of a function? How to compare whether two functions are the same?
(Definition domain, corresponding rule, value domain)
9. What are the common types of finding function domain?
10. How to find the domain of composite function?
The meaning domain is _ _ _ _ _ _ _ _.
1 1. When finding the analytic expression of the function or the inverse function of the function, is the domain of the function marked?
12. What are the conditions for the existence of the inverse function?
(One-to-one correspondence)
Have you mastered the steps of finding the inverse function?
(① Inverse solution x; ② exchange x and y; (3) indicate the domain name)
13. What are the properties of the inverse function?
① the image with reciprocal function is symmetrical about the straight line y = x;
(2) keeping the monotonicity and odd function of the original function;
14. How to prove the monotonicity of a function by definition?
(Take values, make differences, and judge positive and negative)
How to judge the monotonicity of composite function?
∴……)
15. How to judge the monotonicity of a function with derivatives?
The value is ()
A.0 B. 1 C. 2 D. 3
The maximum value of ∴a is 3)
16. What are the necessary (insufficient) conditions for the function f(x) to have parity?
(f(x) domain is symmetric about the origin)
Please note the following conclusions:
(1) In the public domain: the product of two odd function is an even function; The product of two even functions is an even function; The product of even function and odd function is odd function.
17. Are you familiar with the definition of periodic function?
Function, t is a period. )
For example:
18. Have you mastered the common image changes?
Note the following "flip" transformation:
19. Are you familiar with the images and properties of common functions?
The hyperbola of.
Application: ① the relationship between "three quadratic" (quadratic function, quadratic equation, quadratic inequality) and quadratic equation.
② Find the maximum value on the closed interval [m, n].
(3) Find the maximum value of the interval (motion) and the symmetry axis (motion).
④ Distribution of roots of quadratic equation in one variable.