"Proportional Function" PPT download of linear function (the concept of proportional function in Lesson 1)

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"Proportional Function" PPT download of linear function (the concept of proportional function in Lesson 1)

Part One: Learning Objectives

Master the concept of proportional function and be able to judge whether two variables form a proportional function relationship

Be able to find the analytical expression of a proportional function and use it to solve some simple problems (key points and difficulties)

New course introduction

Question: The Beijing-Shanghai high-speed railway, which started operation in 2011, is 1,318km in length.

Assume the average speed of the train is 300 km/h. Consider the following questions:

(1) How many hours does it take to take the Beijing-Shanghai high-speed rail from the originating station, Beijing South Railway Station, to the terminal station, Shanghai Hongqiao Station (the result is rounded to one decimal place)?

(2) What is the quantitative relationship between the journey y (unit: km) and the running time t (unit: h) of the Beijing-Shanghai high-speed rail train?

(3) 2.5 hours after the Beijing-Shanghai high-speed train departs from Beijing South Railway Station, has it passed Nanjing South Railway Station, which is 1,100km away from the departure station?

Proportional function PPT, part 2: knowledge explanation

The concept of proportional function

Thinking: In the following questions, is the corresponding relationship between variables a functional relationship? If yes, please write the analytical expression of the function.

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

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

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

(4) Freeze an object at 0℃ so that it drops by 2℃ every minute. The temperature T (unit: ℃) of the object changes with the change of freezing time t (unit: min).

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.

Why emphasize that k is a constant, k≠0?

Because when k=0, the proportional function y=0×x, that is, y=0, cannot accurately express the relationship between the independent variable and the function, and loses the meaning of the analytical expression.

Proportional function PPT, the third part: training in class

1. Mark “√” if the following statements are correct and “×” if they are incorrect.

(1) If y=kx, then y is a proportional function of x ( )

(2) If y=2x^2, then y is a proportional function of x ( )

(3) If y=2(x-1)+2, then y is a proportional function of x ( )

(4) If y=2(x-1), then y is a proportional function of x-1 ( )

2. Fill in the blanks.

(1) If y=(k-1)x is a proportional function of y with respect to x, then k satisfies _______.

(2) If y=kxk-1 is a proportional function of y with respect to x, then k=____.

(3) If y=3x+k-4 is a proportional function of y with respect to x, then k=_____.

3. If y is a proportional function to x, when x=2, y=-6.

(1) Find the analytical formulas of y and x;

(2) When x=20, find the corresponding function value y.

Proportional function PPT, Part 4 content: Class summary

The concept of proportional function

y=kx（k≠0）

Find the analytical expression of the proportional function

1. Assume 2. Substitute 3. Find 4. Write

Use proportional functions to solve simple practical problems

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For more information about the PPT courseware "The Concept of a Direct Proportional Function and the Concept of a Proportional Function", please click on the PPT tag of "Linear Function PPT Proportional Function PPT Concept of Proportional Function".

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Update Time: 2024-11-09

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