"Inverse Proportional Function" PPT courseware 6

"Inverse Proportional Function" PPT courseware 6

learning target

1. Understand the meaning of the inverse proportional function and master the general form and basic variations of the inverse proportional function.

2. Be able to express some practical problems in life using analytical expressions of inverse proportional functions.

3. Experience the formation process of the inverse proportional function. The experience function is an important model for describing the correspondence between variables.

communication and discovery

Can you list the relationships between the variables in each question?

1. A rectangular lawn with an area of ​​1000m2 is to be planted in a residential area. The length of the lawn y (unit: m) depends on the width x (unit: m). Try to write the analytical function between y and x.

2. Places A and B are 200 kilometers apart. A car drives from place A to place B. Assume the average speed of the car is v kilometers per hour, and the driving time of the car is t hours. Write the distance between v and t. The functional analytical expression of

3. It is known that the product of two real numbers is -10. If one of the factors is P and the other factor is q, try to write the functional relationship between p and q.

collaborative inquiry

Observe the above three functional relationship expressions, and use the group as a unit to discuss what common characteristics they have? Can the general form of this function be written based on what these functions have in common?

Similarities:

①. There are two variables and one constant.

②. They are all in the form of fractions, and one of the variables is in the denominator of the fraction.

General form: y=k/x

In conclusion

Generally speaking, if the functional relationship between variables y and x can be expressed in the form of y=k/x (k is a constant, and k≠0), then y is said to be the inverse proportional function of x.

where k is called the proportional coefficient

y=k/x--y=kx-1--xy=k

Appreciation of examples

Example 1. Assume that the length of one side of a parallelogram with an area of ​​20cm2 is a (cm) and the height of this side is h (cm).

⑴ Find the functional analytical expression of h with respect to a and the value range of the independent variable a;

⑵Is the function of h with respect to a an inverse proportional function? If yes, please state its proportional coefficient

⑶ Find the height of this side when the side length a=25cm.

believe you can do it

1. Write the following functional relationship expressions respectively, and indicate which ones are inverse proportional functions.

(1) When each person plants n trees for a certain amount, the functional relationship between the total number of trees planted y and the number of participants x.

(2) When the distance s between two places is constant, the functional relationship between the time t and the speed v of a student riding a bicycle.

(3) When the pressure F is constant, the functional relationship between the pressure P and the stress area S.

(4) In a certain circuit, when the current I is constant, the functional relationship between the voltage U and the resistance R.

2. It is known that y and x are inversely proportional functions. When x=-3, y=√2; find the analytical formula of the function. y=-3√2/x

Variation 1. It is known that y is inversely proportional to x-2. When x=3, y=2.

Find: (1) The relationship between y and x-2 (2) Find the value of y when x=1.5.

Variation 2: If y+1 is proportional to (x+3)², when x=-2, y=1, find: the value of y when x=1

Compliance in court

1. Which of the following expressions indicate that y is the inverse proportion of x?

Function? and indicate the corresponding value of k in the function.

1. y = 4x; 2. y = 6x+1; 3. xy = 12

2. If y=6x2+n is an inverse proportional function, then n=_______.

3. It is known that y is inversely proportional to x, and when x=3, y=2, then when y=6, x=___

4. You can get a reward of 500 yuan for completing a certain task. Considering that x people will complete the task, try to write the functional analytical formula ______ between the per capita reward y (yuan) and the number of people x (people).

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