"Proportional Function" linear function PPT courseware 2

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"Proportional Function" linear function PPT courseware 2

What kind of function can be used to express the corresponding rules of variables in the following questions?

(1) The circumference l of a circle changes with the size of the radius r.

Solution: l =2πr

(2) The density of iron is 7.8g/cm3. The mass m (unit: g) of the iron block changes with the size of its volume V (unit: cm3).

Solution: m =7.8 V

(3) The thickness of each exercise book is 0.5 cm. The total thickness h (unit: cm) of some exercise books stacked together changes with the change of the number n of these exercise books.

Solution: h = 0.5n

(4) Freeze an object at 0°C so that it drops by 2°C per minute. The temperature T (unit:°C) of the object changes with the freezing time t (unit: minutes).

Solution: T =-2t

induction

Generally, a function of the form y=kx (k is a constant, k≠0) is called a proportional function, where k is called the proportional coefficient.

Think about it, why k≠0?

Which of the two quantities in the following relationship is directly proportional to ( )

(A) The time and speed from point A to point B

(B) The area and side length of the square �

(C) The money required to buy the same exercise book and the number of exercise books

(D) People’s weight and height

Homework assignment:

1. Write the relationship between X and Y in the following questions, and determine whether Y is a proportional function of X?

(1) The telegraph charging standard is 0.1 yuan per word, and the functional relationship between the telegraph fee Y (yuan) and the number of words X (number of words).

(2) The ground temperature is 28°C. If the temperature drops by 5°C for every 1km of increase, then the relationship between temperature X (°C) and altitude Y (km) will be.

(3) The relationship between the circle area Y ( ) and the radius (cm).

2. It is known that y is directly proportional to x-1. When x=3, y=4. Write the functional relationship between y and x, and find the values ​​of y when x=4 and x=-3 respectively.

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Update Time: 2024-11-03

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