精品 高中函数知识点复习总结

精品高中函数知识点复习总结

Chapter 2: ns

I。Concept and n of ns

1.Mapping

1) Mapping: Let A and B be two sets。If there exists a mapping rule f such that for any element in set A。there is a unique element in set B that corresponds to it。then this correspondence (including sets A and B as well as the mapping

rule f) is called a mapping from set A to set B。denoted as f:

A→B.

2) Image and Preimage: Given a mapping from set A to set B。the element b in set B that corresponds to element a in set A is called the image of a。and a is called the preimage of b.

Note: (1) Understanding of the n of mapping。(2) Method to XXX.

2.n

1) n of n

① Original n: XXX variables x and y in a certain process of change。If for every determined value of x within a certain range。there is a unique value of y that corresponds to it。then y is called

a n of x。and x is called the independent variable.

② Modern n: Let A and B be non-empty sets of numbers。and f: x→y be a correspondence rule from A to B。Then the mapping f: A→B from A to B is called a n。denoted as y=f(x)。where x∈A is called the domain of the n。and y∈B is called the range of the n。The set A is called the preimage set。and the set

C⊆B is called the image set.

2) XXX the Concept of n: Domain。Correspondence Rule。and Range.

3.n Methods of n: Analytical Method。List Method。and Graphical Method.

Note: XXX.

II。Analytical n and Domain of n

1.Analytical n of n: An analytical n of a n is a XXX。It is

also called an "analytical n" or an "n," for short。(Note on piecewise ns)

XXX ns:

1) n Method (2) Variable n Method (3) Method of Undetermined Coefficients

4) XXX (5) Parameter Method (6) Real-world Problems

2.Domain of n: The set of values of the independent variable x that make the n meaningful.

XXX Finding the Domain of n:

1) XXX.

2) The radicand of an even root must be non-negative。Zero to the zeroth power is undefined.

3) The base of a logarithmic n must be greater than zero.

4) The base of an XXX n must be greater than zero and not equal to 1.

If a n is XXX。then its domain is the n of the domains of the basic ns.

3.Domain of Composite n: Given that the domain of f(x) is x∈[a,b]。the domain of the composite n f[g(x)] XXX(x)≤b.

III。Range of n

1.n of Range of n: In the n y=f(x)。the set of values of y that correspond to the values of the independent variable x is called the range of the n.

2.Principles for Determining the Range of n:

① When the n y=f(x) is presented in a table。the range of the n refers to the set of real numbers y in the table.

2.函数值域的确定方法：

当给出函数的图像时，函数的值域是指图像在 y 轴上的投影所覆盖的实数集合；当给出函数的解析式时，函数的值域由函数的定义域及其对应法则唯一确定；当函数由实际问题给出时，函数的值域由问题的实际意义确定。

3.求函数值域的方法：

①直接法：从自变量 x 的范围出发，推出 y=f(x) 的取值范围；

②二次函数法：利用换元法将函数转化为二次函数求值域；