"Proportional Function" linear function PPT courseware 3

Description

"Proportional Function" linear function PPT courseware 3

learning target

1. Master the concept of proportional functions.

2. Understand the meaning of the letters in the analytical formula of the proportional function.

3. Able to find the analytical expression of proportional function.

Self-study guidance

Read textbook pages P110-111 and think about the following questions:

1. Think about and solve the questions on page 110.

2. Read and solve the reflection questions on page 111.

3. What common characteristics do the analytical expressions listed in the observation have?

Problem discussion

Question: In 1996, bird researchers bandaged a tern (migratory bird) in Finland; about 128 days later, it was discovered 25,600 kilometers away in Australia.

(1) How many kilometers does this bird weighing more than 100 grams fly on average per day?

25600÷128=200(km)

(2) What is the relationship between the tern’s journey y (unit: kilometers) and the flight time x (unit: days)?

y=200x (0≤x≤128)

(3) How many kilometers does this tern fly for one and a half months (a month is calculated as 30 days)?

When x=45, y=200×45=9000

Use your brain

What kind of function can be used to express the corresponding rules of variables in the following questions? What do these functions have in common?

(1) The circumference L of the circle changes with the change of the radius r;

L=2πr

(2) The density of iron is 7.8g/cm³, and the mass m (unit g) of the iron block changes with its volume V (unit cm³);

m=7.8V

Must do questions

Determine whether the two quantities referred to in the following questions are directly proportional.

(It is to put "√" in the brackets, not to put "×" in the brackets)

(1) Circumference C and radius r ( )

(2) Circle area S and radius r ( )

(3) The distance S and time t in uniform motion ( )

(4) The side area S and the bus length l ( ) of a cone with a base radius r of fixed length

(5) It is known that y=3x-2, y and x ( )

Apply new knowledge

Example 1 (1) If y=5x3m-2 is a proportional function, m=_______.

(2) If y=(m-2)xm²-3 is a proportional function, m=_______.

Example 2 It is known that the base BC of △ABC is 8cm. When the height line on the BC side changes from small to large, the area of ​​△ABC also changes accordingly.

(1) Write the analytical formula of the function of the area y (cm2) of △ABC and the height line x, and indicate what function it is;

(2) When x=7, find the value of y.

Solution: (1) y=1/2×BC×X=1/2×8×X=4X

(2) When x=7, y=4×7=28

Quiz

A school is planning to purchase a batch of basketballs. It is known that the total price y (yuan) of the basketballs purchased is proportional to the number x (pieces). When x=4 (pieces), y=100 (yuan).

(1) Find the proportional function relationship expression and the value range of the independent variable;

(2) Find the value of function y when x=10 (number);

(3) Find the value of the independent variable x when y=500 (yuan).

Solution (1) Assume that the analytical formula of the required proportional function is y=kx,

∵When x =4, y =100, ∴100=4k. Solving for k= 25.

∴The analytical formula of the direct proportional function is y=25x.

The value range of the independent variable x is all natural numbers.

(2) When x=10 (pieces), y=25x=25×10=250 (yuan).

(3) When y=500 (yuan), x=y/25=500/25=20 (pieces).

Summary of this lesson

1. Definition of proportional function

The function y = kx (k is a constant not equal to zero) is called a proportional function.

2. Two methods to find the analytical expression of the proportional function:

(1) Find the analytical formula directly based on the known proportional coefficient

(2) Undetermined coefficient method

3. On the premise of knowing the analytical formula of the proportional function

The value and range of the function---the value and range of the independent variable

Keywords: linear function teaching courseware, direct proportional function teaching courseware, New People's Education Edition eighth grade mathematics second volume PPT courseware, eighth grade mathematics slide courseware download, linear function PPT courseware download, proportional function PPT courseware download, .ppt format

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Update Time: 2024-11-03

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