"Preliminary Understanding of Functions" PPT Courseware 3

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"Preliminary Understanding of Functions" PPT Courseware 3

Review of knowledge points:

Knowledge point 1: Use letters to represent numbers

Using letters to express numbers can concisely express _____ and ________, thus making it easier to describe and research problems.

Notice:

(1) When letters are multiplied by letters, they should be written in the form of ______;

(2) When multiplying numbers and letters, the ____ factor is written in front, and ____ is written in the form of ____;

(3) When dividing the two, the division sign should be written as ________

(4) For questions with units, if the listed formulas are addition and subtraction relationships, they should be enclosed in brackets, such as (2a+3b) yuan.

Knowledge Point 2: Algebraic Formulas

1. Give an example of what an algebraic expression is, _________.

Note: A single number or letter is also an algebraic expression.

2. The key to column algebraic expressions is to clarify the order of operations and correctly understand the quantitative relationship.

3. Replace the letters in the algebraic expression with _________ and operate according to _________. The calculated result is called the value of the algebraic expression.

Notice:

(1) When the numerical factor is a mixed number, it should be converted into ________;

(2) When the coefficient is 1 or -1, 1 should _______;

1. Create situations and introduce problems

1. At the just-concluded 16th Asian Games, Liu Xiang ran a good time of 12.30 seconds. In this competition, his average speed reached 8.5 meters/second. Let’s take a look at his performance in each competition. The distance traveled in one moment.

2. In the long jump competition, according to experience, the distance of the long jump (v is the speed of the run-up, 0

2. Independent exploration, cooperation and exchange

In the following questions, which are variables? Which are constants?

1. Xiao Ming’s brother is a college student. He uses his summer vacation to work in a company, and the salary is 16 yuan/hour. Assume that Xiao Ming’s brother works for t this month, and the compensation he deserves is m yuan.

2. When a long jumper takes a certain take-off posture, the long jump distance (meters) is related to the run-up speed (m/s). According to experience, the long jump distance s = 0.085v2 (0

3. Try to explore and reveal the essence

Do the relationships between the two variables (t and m, s and v) in the above questions have anything in common?

Concept: Generally speaking, in a certain change process, there are two variables x and y. If for every certain value of x, y has a unique certain value, then y is said to be a function of x, and x is called Independent variable.

function value concept

For the function m=7.8t, when t=5, can the value of m be found? How to ask for it?

Substituting this into the functional analytical formula, we get m=7.8t=7.8×5=39

Function value: Here, we call m=39 the function value when the independent variable t=5.

Effect detection

①The relationship between the following variables is not a functional relationship ( )

A. The length of one side of the rectangle is 6 cm, and the relationship between its area S cm and the length of the other side x cm

B. The relationship between the area and perimeter of a square

C. The relationship between the area and circumference of a circle

D. The relationship between the area of ​​a certain figure and the position of the plane on which it is located

②Generally, if there are two _________ in a___________, such as x and y, for each value of x, y has a _________ corresponding to it, we say that x is___________, y is ___________, at this time it is also said that y is __________ of x

Through the above exercises, you must know functions and independent variables? Communicate with your deskmates to find out the connections and differences between them.

Tips: 1. There must be two variables

2. Every time the independent variable takes a value, the function has a unique corresponding value.

Learning summary

1. What knowledge have you learned? What should we pay attention to?

2. What experience did you have during the learning process?

Classroom testing station

1. Give three examples of functional relationships encountered in daily life.

Answer: (1)_______________________________;

(2)____________________________________;

(3)______________________________.

2. In the function y=-3x +7, when x=2, the function value is ( )

A． 3B． 2C. 1 D． 0

3. Write the following functional relationship expressions and indicate the independent variables and functions.

A car leaves Nanjing and drives on the highway to Shanghai at a speed of 120km/h. The distance from Nanjing to Shanghai is about 270km. Then the functional relationship between the distance s of the car from Shanghai and the driving time t;

4. Print a rectangular poster (as shown in Figure 17-5). Its printing area is 1dm at the top and bottom, and 0.5dm at both sides. Assume that the length of the printed part from top to bottom is x dm, and the surrounding blank area is For S, find the functional relationship between S and x, and find the value of S when x=8dm.

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"Preliminary Understanding of Functions" PPT courseware 4:

"Preliminary Understanding of Functions" PPT Courseware 4 Learning Objectives 1. Combined with examples, know the meaning of independent variables and functions, and be able to distinguish independent variables and functions. 2. For a given function, be able to find the value of the function based on the value of the independent variable . [Learning Key Points and Difficulties] Key Points: Right...

"Preliminary Understanding of Functions" PPT Courseware 2:

"Preliminary Understanding of Functions" PPT Courseware 2 [Knowledge Review] 1. The relationship between the perimeter c and the side length a of a square is _________, where the constant is ____________ and the variable is ____________. 2. If r is used to represent a circle Radius, S represents the area of ​​the circle, then...

"Preliminary Understanding of Functions" PPT courseware:

"Preliminary Understanding of Functions" PPT courseware [Knowledge Review] 1. The relationship between the perimeter c and the side length a of a square is ____________, where the constant is ____________ and the variable is ______________. 2. If r is used to represent the radius of a circle , S represents the area of ​​the circle..

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Update Time: 2024-10-05

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 1 industry PPT template

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