"The Concept and Representation of Function" The Concept and Properties of Function PPT (The Concept of Function in the First Lesson)

Description

"The Concept and Representation of Function" The Concept and Properties of Function PPT (The Concept of Function in the First Lesson)

Part One: Learning Objectives

Understand the concept of function and the three elements that constitute a function

Can find the domain of some simple functions and use intervals to express them

Master the same function and be able to judge

Be able to find the function value and range of simple functions, and use intervals to express the range.

The concept of function and its representation PPT, part 2: independent learning

Problem guide

Preview the textbook P60-P66 and think about the following questions:

1. What is the definition of function?

2. How are the independent variables and domain of a function defined?

3. How is the range of a function defined?

4. What is the concept of interval? How to represent a number set using intervals?

A preliminary exploration of new knowledge

1. Concepts related to functions

■Instructions from famous teachers

3 points on the concept of functions

(1) When A and B are non-empty number sets, the symbol f: A→B represents a function from set A to set B.

(2) The numbers in set A are arbitrary, and the numbers in set B are unique.

(3) The symbol "f" represents the corresponding relationship. The specific meaning of f in different functions is different.

2. The concept and representation of interval

(1)Interval definition and representation

Suppose a and b are two real numbers, and a

(2) The concept of infinity and the representation of infinite intervals

■Instructions from famous teachers

2 points about infinity

(1) "∞" is a symbol, not a number.

(2) When "-∞" or "+∞" is used as the endpoint, this end of the interval must be in parentheses.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) A functional relationship can be established between any two sets. ()

(2) A function can be determined if the domain and corresponding relationship are known. ()

(3) According to the definition of the function, each x in the domain of definition can correspond to a different y.()

(4) The interval can represent any set. ()

It is known that the function g(x)=2x2-1, then g(1)=()

A． -1　B． 0

C. 1D． 2

The concept of function and its representation PPT, the third part: lecture and practice interaction

The concept of function

(1) As shown in the figure, what can be used as the image of the function y=f(x) is ()

(2) The following three statements:

①If the value domain of the function contains only one element, the domain also contains only one element;

②If f(x)=5(x∈R), then f(π)=5 must be true;

③A function is the correspondence between two sets.

The number of correct statements is ()

A． 0B. 1

C. 2D． 3

(3) It is known that set A=[0,8] and set B=[0,4], then the following correspondence cannot be regarded as a functional relationship from A to B of is()

A． f：x→y＝18x B． f：x→y＝14x

C. f：x→y＝12x D. f：x→y＝x

regular method

(1) Method to determine whether the given correspondence is a function

① First observe whether the two number sets A and B are non-empty;

② Verify the arbitrariness of x in set A and the uniqueness of y in set B under the corresponding relationship.

(2) Steps to determine whether the corresponding relationship is a function based on the graph

① Take any straight line l perpendicular to the x-axis;

② Move the straight line l parallelly within the definition domain;

③If l has one and only one intersection point with the graph, it is a function; if there is no intersection point or two or more intersection points within the definition domain, it is not a function.

Track training

1. The following graph can represent the function with M={x|0≤x≤1} as the domain and N={y|0≤y≤1} as the value range: ()

2. Which of the following correspondences is a function on the set P?

①P=Z, Q=N*, corresponding relationship f: The absolute value of the elements in the set P corresponds to the elements in the set Q;

②P={-1,1,-2,2}, Q={1,4}, corresponding relationship f: x→y=x2, x∈P, y∈Q;

③P={triangle}, Q={x|x>0}, corresponding relationship f: finding the area of ​​the triangle in P corresponds to the elements in the set Q.

Find the domain of a function

Find the domain of the following functions:

(1)y=(x+1)2x+1-1-x; (2)y=3-x|x|-5.

regular method

(1) Common methods for finding the domain of a function

①If f(x) is a fraction, you should consider making the denominator non-zero;

②If f(x) is an even-order radical, the radicand is greater than or equal to zero;

③If f(x) is an exponential power, the domain of the function is the set of real numbers that make the power operation meaningful;

④If f(x) is composed of several formulas, then the domain of the function is the intersection of several partial domains;

⑤If f(x) is the analytical formula of the actual problem, it should be consistent with the actual problem to make the actual problem meaningful.

(2) In question (1), it is easy to simplify y = x + 1 - 1 - x, and the domain of the function is found to be {x|x≤1}. When finding the domain of a function, the functional formula cannot be blindly deformed.

The concept of function and its representation PPT, Part 4: Feedback on achievement of standards

1. If f(x)=x+1, then f(3)=()

A． 2B. 4

C. 22D. 10

2. For function f: A→B, if a∈A, then the following statement is wrong ()

A． f(a)∈B

B． f(a) has and only one

C. If f(a)=f(b), then a=b

D. If a=b, then f(a)=f(b)

3. If [0,3a-1] is a definite interval, then the value range of a is ________.

4. Represent the following sets of numbers as intervals:

(1){x|x≥1}=________;

(2){x|2

(3){x|x>-1 and x≠2}=________.

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Update Time: 2024-06-19

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