"Image of Function" PPT courseware

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"Image of Function" PPT courseware

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1. The car is traveling at a constant speed of 60 kilometers/hour, the driving mileage is s kilometers, and the driving time is t hours, then the functional relationship between s and t is S=60t;

2. The table on the right is my country’s demographic table. Is the population y a function of year x?

3. The picture shows an electrocardiogram during a physical examination. The abscissa x represents time, and the ordinate y represents the bioelectric current in the heart. Is y a function of x?

Knowledge link

1. In a certain problem, a quantity that remains unchanged is called a constant, and a quantity that can take on different values ​​is called a variable.

2. Function: In the same change process, there are two variables x and y. If for each value of x, y has a unique value corresponding to it, we call y a function of x, where x is called Independent variable. If the value of y is b when the independent variable x is a, then b is called the function value when x=a.

3. Plane rectangular coordinate system: Draw two mutually perpendicular number axes with a common origin in the plane. The horizontal one is called the x-axis or the horizontal axis. It is customary to point to the right direction as the positive direction. The vertical one is called the y-axis or the vertical axis. axis, the direction on the orientation is the positive direction, which forms a plane rectangular coordinate system.

Observe this curve and think about the following questions:

(1) From the time the water is released to the time it is released for 10 seconds, how much does the water surface in the beverage bottle drop? What about from 10 seconds after the water is released to 20 seconds after the water is released?

(2) As the water release time t gradually increases, what is the changing trend of the height L of the water surface in the beverage bottle?

(3) Every time t increases by 10 seconds, does L change in the same way?

(4) Estimate what is the value of L when t=55s? How did you estimate that?

It is estimated that when t=55s, the value of L is 25 (mm), which is estimated from the image and table.

(5) Did you find that during the change of the water surface drop height L and the water release time t, is L a function of t? Which variable is the independent variable?

How is the functional relationship between them expressed?

New knowledge exploration

The picture below is a curve of day and night temperature changes recorded by a weather station on a certain day. Please answer the following questions based on this picture:

(1) What is the temperature T at 6 o'clock, 8 o'clock and 20 o'clock on this day?

(2) How to determine the temperature T at a certain time t on this day?

(3) What relationship between two variables does this curve reflect?

(4) Please find the highest and lowest points on the curve. Can you tell the coordinates of these two points respectively? Can you explain what the coordinates of these two points actually mean?

(5) How did the temperature change from 4:00 to 14:00? How does the curve depict this change?

(6) What other information can you get from the picture?

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

Example 1: Xiao Liang walks from home to the bookstore, spends a period of time choosing the books he needs, and then returns home. The functional relationship between Xiao Liang’s distance from home and the time since he left home is as shown in the figure. Answer based on the image The following questions:

(1) How long does it take Xiaoliang to walk to the bookstore? (20 minutes) How far is Xiaoliang’s home from the bookstore? (900 meters)

(2) How long did Xiaoliang stay in the bookstore? (20 minutes) How long did it take to get home? (15 minutes)

(3) What is Xiaoliang’s walking speed to the bookstore and home?

(45m/min, 60m/min)

(4) How far is Xiaoliang from home in 10 minutes?

How far is it from home in 50 minutes?

Two engineering teams A and B participate in the same water conservancy construction project. Figure 10-4 is a function image of the earthwork volume V (m3) constructed by engineering teams A and B and the construction time t (days) drawn in the Cartesian coordinate system. Please answer the following questions based on the image:

(1) How many days before Engineering Team B starts construction 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) In which period of time did Engineering Team A make the fastest progress?

(4) What other information can you get from the image?

Keywords: image teaching courseware of functions, Qingdao edition eighth grade mathematics volume PPT courseware download, eighth grade mathematics slide courseware download, image of function PPT courseware download, .PPT format;

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Update Time: 2024-07-05

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

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