"Application of Functions" PPT courseware on the concept and properties of functions

Description

"Application of Functions" PPT courseware on the concept and properties of functions

Part One: Learning Objectives

1. Understand the wide application of function models (such as linear functions, quadratic functions, piecewise functions and other function models commonly used in social life).

2. Be able to use a given function model or establish a certain function model to solve practical problems. (main difficulty)

core competencies

1. Solve practical problems by establishing function models and cultivate mathematical modeling literacy.

2. Improve mathematical operation literacy with the help of optimal value problems in practical problems.

Application of functions PPT, part 2: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

Common types of function models

Function model Function analytical expression

Linear function model f(x)=ax+b(a, b are constants, a≠0)

Quadratic function model f(x)=ax2+bx+c (a, b, c are constants, a≠0)

Piecewise function model f(x)＝f1x,x∈D1f2x,x∈D2……fnx,x∈Dn

First try

1. The perimeter of a rectangle is 40, then the analytical formula of the function of the length y of the rectangle with respect to the width x is ()

A． y＝20－x,0

B． y＝20－2x,0

C. y＝40－x,0

D. y＝40－2x,0

2. The image of the change of the driving distance s of a car in a certain distance with respect to time t is as shown in the figure, then the function model corresponding to the image is ()

A． linear function model

B． quadratic function model

C. piecewise function model

D. unconfirmed

3. The purchase unit price of a store is 45 yuan. If it is sold at 50 yuan each, 50 units can be sold. If the sales unit price increases by 1 yuan, the sales volume will decrease by 2 units. In order to obtain the maximum profit, the best selling price of this product should be For each _________ yuan.

Application of functions PPT, the third part: cooperative exploration to improve literacy

Application of linear function model

[Example 1] The relationship between the total daily production cost of stationery boxes y (yuan) and the daily output x (sets) of a factory is y = 6x + 30 000. The ex-factory price is 12 yuan per set. To prevent the factory from losing money, At least daily production of stationery boxes ()

A． 2,000 sets B. 3 000 sets

C. 4,000 sets D． 5 000 sets

regular method

1. Practical application of linear function model

When applying the primary function model, the principle of "ask what, assume what, list what" is followed.

2. Optimal solution of a linear function

Finding the maximum value of a linear function is often transformed into solving the inequality ax + b ≥ 0 (or ≤ 0). When solving, pay attention to the sign of the coefficient a. You can also combine the function graph or its monotonicity to find the maximum value.

Track training

1. As shown in the figure, this is the functional relationship between the telephone fee y (yuan) and the call time t (minutes) stipulated by a certain communication company to make a certain international long-distance call. Fill in the blanks based on the image:

①If the call lasts for 2 minutes, you need to pay the phone fee of ________ yuan;

②If the call lasts for 5 minutes, you need to pay the phone fee _________ yuan;

③If t≥3, then the functional relationship between the telephone fee y (yuan) and the call time t (minutes) is _________.

①3.6　②6　③y＝1.2t(t≥3)　①It can be seen from the image that when t≤3, the telephone fee is 3.6 yuan.

② It can be seen from the image that when t=5, y=6, the phone bill needs to be 6 yuan.

③It is easy to know that when t≥3, the image passes through points (3,3.6), (5,6), and the undetermined coefficients are found to be y=1.2t (t≥3). ]

Application of Quadratic Function Model

[Example 2] A fruit wholesaler sells apples with a purchase price of 40 yuan per box. Assume that the selling price per box shall not be less than 50 yuan and shall not be higher than 55 yuan. Market research found that if each box is sold at a price of 50 yuan, an average of 90 boxes will be sold per day. For every price increase of 1 yuan, an average of 3 boxes will be sold per day.

(1) Find the functional relationship between the average daily sales volume y (box) and the sales unit price x (yuan/box);

(2) Find the functional relationship between the wholesaler’s average daily sales profit w (yuan) and the sales unit price x (yuan/box);

(3) When the selling price of each box of apples is how much, the maximum profit can be obtained? What is the maximum profit?

[Ideas] In this question, the average daily sales volume y (box) and the sales unit price x (yuan/box) are a linear function relationship. Although x∈[50,55], x∈N, but the problem can still be regarded as an application problem of a linear function model; the average daily sales profit w (yuan) and the sales unit price x (yuan/box) are a quadratic functional relationship, which can be regarded as a quadratic Application problems of functional models.

regular method

The analytical formula of the quadratic function model is g(x)=ax2+bx+c(a≠0). In function modeling, it occupies an important position. After establishing the analytical formula of the function based on actual problems, the combination method and the discriminant method can be used , substitution method, monotonicity of function and other methods to find the optimal value of the function, thereby solving the optimal value problem in practical problems. Finding the optimal value of a quadratic function is best solved by combining the image of the quadratic function.

Class summary

1. To solve problems related to functions, you should first consider which function to choose as a model, and then establish its analytical formula. When finding analytical expressions, the undetermined coefficient method is generally used. It is necessary to fully explore the implicit conditions of the question and make full use of the intuitiveness of function graphics.

2. The process of mathematical modeling is illustrated as follows:

PPT on the application of functions, part 4: meeting the standards in class and solidifying the base

1. Thinking and analysis

A and B are running in a race. The functional relationship between distance s and time t is as shown in the figure. Determine whether the following statements are true or false.

(1) A sets off before B. ()

(2) B has traveled more distance than A. ()

(3) A and B have the same speed. ()

(4)A reaches the finish line first. ()

2. Fill a water bottle with a height of H until it is full. If the graph of the functional relationship between the water injection volume V and the water depth h is as shown in the figure, then the shape of the water bottle is ()

3. If someone starts from point A, drives a car at a speed of 80 kilometers/hour to point B in 2 hours, and stays in point B for 2 hours, then the distance y (unit: kilometers) of the car from point A is time t (unit: : hour) function, the analytical formula of this function is ________.

4. The functional relationship between the daily profit of a certain amusement park, y yuan, and the number of tickets sold, x, is as shown in the figure. Try to solve the following problems using the image:

(1) Find the analytical formula of the function of y and x;

(2) To make the amusement park's daily profit exceed 1,000 yuan, how many tickets must be sold every day?

Keywords: Free download of compulsory PPT courseware for High School People's Education A version of mathematics, PPT download of application of functions, PPT download of concepts and properties of functions, .PPT format;

For more information about the "Application of Functions, Concepts and Properties of Functions" PPT courseware, please click on the "Applications of Functions ppt Concepts and Properties of Functions" ppt tag.

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Update Time: 2024-11-20

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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