"Image of Function" PPT Courseware 2

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"Image of Function" PPT Courseware 2

review review

1. Three representation methods of functions

Analytical method List method Image method

2. Image method

The method of using images to represent functional relationships between variables is called the image method

3. There is a one-to-one correspondence between points in the coordinate plane and ordered pairs of real numbers.

Try your hand

The process reflected in the picture below is that Xiao Ming went from home to water the vegetable field, then went to the corn field to weed, and then returned home. Among them, x represents time, and y represents the distance between Xiao Ming and his home. Xiao Ming's home, vegetable field, and corn field are on the same straight line.

Can you answer the following questions?

1. How long does it take to get from home to the vegetable field? How far is the vegetable field from Xiao Ming’s house?

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

3. How long does it take to get from the vegetable field to the corn field? How far is the vegetable field from the corn field?

4. How long did Xiao Ming spend weeding the cornfield?

5. How far is the cornfield from home? What is Xiao Ming’s average speed returning home from the cornfield?

Example 1 Before using a household shower, the amount of water in the water tank is 0L. When using it, first fill the water tank with water. After filling the water, turn off the water source and turn on the electricity for heating. When the heating is completed, cut off the power supply and start showering. The water will be released at a constant speed until Use up the water in the water tank. During this process, the function graph of the water storage volume V (L) of the water tank in the shower versus time t (min) is shown in Figure 10-3. Answer the following questions based on the graph:

(1) How long does it take to fill the water, heat and shower?

(2) What is the maximum water storage capacity of the water tank?

(3) How many liters of water are left in the water tank 15 minutes after the shower starts?

Two engineering teams A and B participate in water conservancy construction. The function image of the amount of earthwork and the time used for the two pairs of construction is as shown in the figure. Please answer the questions based on the image:

(1) How many days later does Engineering Team B start work than Engineering Team A? How many days early will it be finished?

(2) How many days did engineering team A rest during the construction?

(3) During which time period did Engineering Team A make the fastest progress?

(4) What other information can you get about the construction work of engineering teams A and B from the images?

practice

Answer the following questions based on the image:

(1) How long did Xiao Ming spend eating breakfast in the canteen?

(2) How far is the cafeteria from the library? How long did it take Xiao Ming to get from the cafeteria to the library?

(3) How long did it take Xiao Ming to read the newspaper?

(4) How far is the library from Xiao Ming’s home? What is the average speed at which Xiao Ming returns home from the library?

Experimentation and inquiry

Let's explore the graph of the function y=x-1.

(1) Given some values ​​of x for the independent variable, find the corresponding value of y and fill in the table;

(2) Use the corresponding values ​​​​of x and y as the coordinates of the points to draw these points;

(3) Connect the traced points in order from small to large independent variables.

As shown in the figure, the image of the function y=x-1 can be obtained.

Steps to draw function images using the point tracing method: ① list ② tracing points ③ connecting lines

communication and discovery

Think about it, which of the following points are on the graph of the function y=x-1? Why?

A (-1.5, -2.5) B (-10, -9)

C (100, 99) D (200, 201)

Summary:

If the point is on the function graph, the coordinates of the point satisfy the analytical expression of the function. Otherwise, the point that satisfies the analytical expression must be on the function graph.

practice

1. The known point (-1,2) is a point on the graph of function y=kx, then k=______.

2. Among the following points, what is on the graph of function y=√x ( )

A. (-2,-4) B. (4,4) C. (-2,4) D. (4,2)

3. Point A (1, m) is on the graph of function y=2x, then the coordinates of the point are ( )

A. (1,) B. (1,2) C. (1,1) D. (2,1)

4. Among the following four points, there are ( ) on the graph of function y=2x-3.

(1,2) , (3,3) , (—1, —1), (1.5,0)

A． 1 B.2 C.3 D.4

Summary and improvement

1. The horizontal and vertical coordinates of the points on the function graph correspond to the _____ value and the _____ value respectively.

2. The key to studying practical problems from the information obtained from the function graph is to distinguish the actual meaning of the horizontal and vertical axes.

3. Steps to draw function image using point tracing method:

①List ②Draw points ③Connect lines

4. If the point is on the function graph, the coordinates of the point satisfy the analytical expression of the function. Otherwise, the point that satisfies the analytical expression must be on the function graph.

Classroom testing

1. One morning, Xiao Ming left home for a run to the park to exercise for a while and then returned home. In the image below, the functional relationship between Xiao Ming’s distance y from home and time x is ( ).

2. Which of the following points are on the graph of function y=2x-1?

A(1,-2) B(-2.5,-6) C(0,-1)

D(101,199)E(-100,-103)F(1.5,2)

Classroom testing

The image in the figure (broken line ABCDE) describes the functional relationship between the distance s (kilometers) of the car from the starting point and the driving time t (hours) during the driving of a car on a certain straight line. According to the figure The information provided in , gives the following statement:

①The car traveled a total of 120 kilometers; ②The car stayed for 0.5 hours while driving;

③The average speed of the car during the entire driving process is 80/3 kilometers/hour;

④The driving speed of the car gradually decreased between 3 hours and 4.5 hours after departure.

The correct statement among them is total ( )

A. 1 B. 2 C. 3 D. 4

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Update Time: 2024-10-14

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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