"Representation of Functions" PPT courseware

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"Representation of Functions" PPT courseware

Part One Content: Learning Objectives:

1. Be able to use the point drawing method to draw simple function graphs, and understand the relationship between the three expression forms of functions through examples.

2. Be able to combine function images and understand the changes of functions.

3. Integrate the idea of ​​combining numbers and shapes, and learn the basic drawing methods of function images.

Focus: How to draw function graphs.

Difficulty: Understand the connection between the three expression forms of functions.

Self-learning

Self-study textbook pages 69 to 71

Initial understanding of the relationship between the three expressions of functions.

Get a preliminary understanding of the steps to draw the graph of a function.

Representation of functions PPT, part 2: cooperation and communication

Questions: 1. Can you write the functional relationship between the side length x and the area S of the square, and determine the value range of the independent variable x?

S=x2 The value range of the independent variable x is x>0

2. Can we use the method of drawing in the coordinate system to express the relationship between S and x?

Tip: A certain value of the independent variable x and its corresponding function value S determine a point (x, S)

Representation of function PPT, the third part: the definition of function image

Generally speaking, for a function, if each pair of corresponding values ​​​​of the independent variable and the function is used as the horizontal and vertical coordinates of the point, then the graph composed of these points in the coordinate plane is called the image of the function.

(1) How to draw the graph of a function?

① Establish a plane rectangular coordinate system, using the horizontal axis to represent the independent variable x and the vertical axis to represent the function value y.

② Use tables (or expressions) to find several pairs of corresponding values ​​​​of x and y, and use each pair of values ​​​​as the horizontal and vertical coordinates to determine the corresponding point in the coordinate system

③ Connect these points with smooth lines to get the graph of the function.

(2) What are the characteristics of the image method?

Representation of functions PPT, Part 4: Consolidation exercises

1. The price of tomatoes in a vegetable market is 2 yuan/kg. Assume that the mass of tomatoes purchased is X kilograms, and the payment payable is y yuan.

Question 1: Please write the functional expression of y changing with x, and indicate the value range of the independent variable.

Question 2: Please draw the graph of this function.

2. The following image reflects the process: Xiao Ming sets out from home to water the vegetable field, then goes to the corn field to weed, and then returns home. Among them, x represents the time and y represents the distance between Xiao Ming and his home.

(1) How far is the vegetable field from Xiao Ming’s house? How long did it take Xiao Ming to walk to the vegetable patch?

Viewed from the ordinate: the vegetable field is 1.1 kilometers away from Xiao Ming’s house.

Looking at the abscissa: it took Xiao Ming 15 minutes to walk to the vegetable patch.

(2) How long did it take Xiao Ming to water the vegetable field?

Looking at the abscissa: Xiao Ming spent 10 minutes watering the vegetable field (i.e. 25-15)

(3) How far is the vegetable field from the corn field? How long did it take Xiao Ming to walk from the vegetable field to the corn field?

Viewed from the ordinate: the vegetable field is 0.9 kilometers away from the corn field.

Looking at the abscissa: it took Xiao Ming 12 minutes to go from the vegetable field to the corn field.

(4) How long did Xiao Ming spend weeding the cornfield?

Looking at the abscissa: Xiao Ming spent 18 minutes weeding the corn field (i.e. 55-37)

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, Representation of function PPT download, .PPT format;

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Update Time: 2024-11-18

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