"Inverse Proportional Function" PPT courseware 4

Description

"Inverse Proportional Function" PPT courseware 4

Preliminary question assessment

1. What is a function? Can you give examples?

In a certain change process, there are two variables x and y. If the value of one of the variables x is given and y has a unique value corresponding to it, then y is said to be a function of x.

2. The expression of a linear function is Y=kx+b, where k and b are constants and k≠0

3. The expression of the proportional function is Y=kx, where k is a constant that is not 0.

4. The distance from A to B is 1200km. A person drives from A to B. The relationship between the car’s speed V (km/h) and time t (h) is vt=1200 then t In =_______, is the relationship between t and v the relationship between a proportional function and a linear function? What is the relationship between them?

think about it

1. Why does stage lighting change a bright sunny day into a cloudy day with thick clouds, or from night to day in a short period of time?

Solution: When R becomes larger, I becomes smaller and the light becomes darker. When R becomes smaller, I becomes larger and the light becomes brighter. Therefore, by changing the size of the resistor R to control the change of the current I, you can control the change of the current I in a very short time. It can change a bright sunny day into a cloudy day with dense clouds, or from night to day within a certain period of time.

2. The total length of the Beijing-Shanghai Expressway is 1262km. A car drives from Shanghai to Beijing along the Beijing-Shanghai Expressway. What is the relationship between the time t (h) it takes for the car to complete the journey and the average driving speed v (km/h)? Relationship? Is the variable t a function of v? Why?

Solution: The relationship between variables v and t can be expressed as t=1262/v

When a value of V is given, a value of t is determined accordingly, so t is a function of v

Inverse proportional function: Generally, if the relationship between two variables x and y can be expressed in the form of y=k/X or y=kx-1 (k is a constant, k≠0), then y is said to be the inverse proportion of x function.

The argument of the inverse proportional function is not 0

Practice in class

1. In the following function expressions, x all represents independent variables, so which ones are inverse proportional functions? What is the corresponding k value of each inverse proportional function?

(1)y=5/x (2)y=0.4/x (3)y=x/2 (4)xy=2

2. Can you give an example of an inverse proportional function? Communicate with your peers.

Do it

1. The area of ​​a rectangle is 20cm2 and the adjacent side lengths are xcm and ycm. So is the variable y a function of the variable x? Is it an inverse proportional function? Why?

Solution: From the area equal to the length times the width, we can get xy=20, then y=20/x. The variable y is a function of x, because given a value of x, a value of y is determined accordingly. According to the definition of the function, it can be seen that the variable y is a function of the variable x, and according to the expression of the inverse proportional function, we can know that y is the inverse proportional function of x.

2. A certain village has 346.2 hectares of cultivated land, and the population n changes year by year. So is the per capita cultivated land area m (hectare/person) in the village a function of the village’s population n? Is it an inverse proportional function? Why?

3. y is the inverse proportional function of x. The following table gives some values ​​of x and y:

(1)Write the expression of this inverse proportional function

Solution: Let the expression of the inverse proportional function be y=k/x

∵When x=-1, y=2

∴k=-2

∴The expression is y=-2/x

(2) Complete the above table according to the function expression

Keywords: Inverse proportional function teaching courseware, New People's Education Edition eighth-grade mathematics volume PPT courseware, eighth-grade mathematics slide courseware download, inverse proportional function PPT courseware download, .ppt format

For more information about the "Inverse Proportional Function" PPT courseware, please click the Inverse Proportional Function ppt tab.

"Image and Properties of Inverse Proportional Functions" PPT courseware:

"Image and Properties of Inverse Proportional Functions" PPT courseware draws the image of the inverse proportional function y=6/x. 1. List: 2. Draw points: Use the corresponding values ​​​​of each group in the table as the coordinates of the points, and draw the corresponding values ​​​​in the plane rectangular coordinate system point. 3. Connection: Use smooth curves to connect each...

"Application of Inverse Proportional Functions" PPT courseware:

"Application of Inverse Proportional Functions" PPT courseware uses the knowledge of inverse proportional functions to solve practical problems. The general idea can be roughly divided into the following two steps: (1) Carefully review the question and establish the inverse proportional function ________; (2) Based on the known conditions, find the solution from a variable ______________..

"Inverse Proportional Function" PPT courseware 8:

"Inverse Proportional Function" PPT courseware 8 1. A function of the form ________(k is a constant, and k0) is called an inverse proportional function, where k is called _________. 2. The value range of the independent variable x in the inverse proportional function is______. 1. (4 points) The following functions are inversely proportional functions..

File Info

Update Time: 2024-11-11

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

Preview