"The Concept and Representation of Functions" PPT courseware on the concepts and properties of functions (the representation of functions in the second lesson)

Description

"The Concept and Representation of Functions" PPT courseware on the concepts and properties of functions (the representation of functions in the second lesson)

Part One: Learning Objectives

1. Master the three representation methods of functions: analytical method, graphical method, and list method. (emphasis)

2. Will choose the appropriate method to represent functions according to different needs. (difficulty)

core competencies

1. Cultivate intuitive imagination literacy through the image method of functional representation.

2. Cultivate operational literacy through finding analytical expressions of functions.

The concept of function and its representation PPT, the second part: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

function representation

Thinking: Can any function be expressed in three forms: analytical method, list method, and diagram method?

Tip: Not necessarily.

Not all functions can be expressed by analytical expressions. Not only that, the image method is not suitable for all functions, such as D(x)=0, x∈Q, 1, x∈∁RQ. Although the list method is theoretically It is applicable to all functions, but for situations where the independent variable has countless values, the list method can only represent an overview or fragment of the function.

First try

1. It is known that the function f(x) is given by the following table, then f(3) is equal to ()

x 1≤x<2 2 2

f(x) 1 2 3

A.1B. 2C． 3D． does not exist

2. The vertex of the graph of the quadratic function is (0, -1), and the symmetry axis is the y-axis. Then the analytical formula of the quadratic function can be ()

A． y=-14x2+1

B． y=14x2-1

C. y=4x2-16

D. y=-4x2+16

3. It is known that the graph of function y=f(x) is as shown in the figure, then its domain is ______.

The concept of function and its representation PPT, the third part of the content: cooperative exploration to improve literacy

Three ways to represent functions

[Example 1] A shopping mall has newly purchased 10 color TV sets, each priced at 3,000 yuan. Try to find the functional relationship between the number of units sold x and the number of payments y. Use the list method, image method, and analytical method to express come out.

[Solution]①The list method is as follows:

②Image method: As shown in the figure.

③Analytical method: y=3 000x, x∈{1,2,3,…,10}.

regular method

List method, image method and analytical method describe the corresponding relationship between independent variables and function values ​​from three different perspectives. The same function can be expressed in different ways. Pay attention when using three methods to express functions: ① The analytical method must indicate the domain of the function; ② The independent variables selected in the list method must be representative and should reflect the characteristics of the domain; ③ Pay attention to the graphical method Is it connected?

Tracking method

1. (1) A student left home to go to school. He started running and then walked the rest of the distance when he was tired. In the following figure, the vertical axis represents the distance from school, and the horizontal axis represents the time since departure. The one that is more consistent with the student's walking method is ()

(2) The function y=f(x) is given by the following table, then f(f(1)) is equal to ()

x 1 2 3 4 5

y 4 5 3 2 1

A.1　B． 2

C. 4D. 5

(1)D　(2)B　(1) Based on the meaning of the question, it can be seen that the distance of the student from school first decreases rapidly, then decreases slowly, and finally reaches 0, so D is selected.

(2) From the meaning of the question, we can see that f(1)=4, f(4)=2, ∴f(f(1))=f(4)=2, so choose B.]

Image drawing methods and applications

[Example 2] Make the graph of the following function and find its value range.

(1)y=-x, x∈{0,1,-2,3}; (2)y=2x, x∈2,+∞); (3)y=x2+2x, x∈& #091;-2,2).

regular method

Three points of concern when constructing function graphs using the point tracing method

1When drawing the graph of a function, first pay attention to the domain of the function, that is, draw the graph within the domain.

2The image is a solid line or a real point, and the parts outside the definition domain can sometimes be used as a dotted line to set off the entire image.

3 Mark certain key points, such as the vertices, endpoints of the image, intersections with the coordinate axes, etc. It is necessary to distinguish whether these key points are solid points or open circles.

Reminder: The function graph can be a continuous curve, a straight line, a polyline, a discrete point, etc.

The concept of function and its representation PPT, the fourth part: reaching the standard in class and solidifying the double base

1. Thinking and analysis

(1) Any function can be expressed analytically. ()

(2) The graph of the function must be a continuous curve on the defined interval. ()

2. It is known that the function f(x+1)=3x+2, then the analytical formula of f(x) is ()

A． f(x)=3x-1

B． f(x)＝3x＋1

C. f(x)=3x+2

D. f(x)＝3x＋4

3. The known functions f(x) and g(x) are given by the following table respectively.

Then g(f(5))=________; f(g(2))=________.

Keywords: Free download of PPT courseware for compulsory course No. 1 Mathematics of High School People's Education A version, PPT download of the concept of function and its representation, PPT download of the concept and properties of function, PPT download of representation of function, .PPT format;

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Update Time: 2024-10-03

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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