"Application of Functions" Concept and Properties of Functions PPT

描述

"Application of Functions" Concept and Properties of Functions PPT

Part One: Learning Objectives

Will build a function model to solve practical problems

Can build quadratic function models to solve practical problems

Can use it to solve practical problems related to power functions

Can use piecewise functions to solve practical problems related to them

Application of functions PPT, part 2: lecture, practice and interaction

linear function model

In order to develop the telecommunications industry and facilitate users, telecommunications companies adopt different charging methods for mobile phones. The "Ruyi Card" and "Convenience Card" used within a certain city have a monthly (30 days) call time of x (unit: The relationship between cents) and call cost y (unit: yuan) is as shown in the figure:

(1) Find the functional analytical expressions between the call costs y1, y2 and the call time x respectively;

(2) Please help users calculate which card is cheaper to use within a month.

regular method

When using a linear function model to solve practical problems, you need to pay attention to the following two points:

(1) The undetermined coefficient method is a common method for finding the analytical expression of a linear function.

(2) When the coefficient of the linear term is positive, the linear function is an increasing function; when the coefficient of the linear term is negative, the linear function is a decreasing function.

Track training

A train runs from Beijing West Railway Station to Shijiazhuang, with a total distance of 277 km. The train departs for 10 minutes and travels 13 km, and then travels at a constant speed of 120 km/h. Try to write down the functional relationship between the total distance s traveled by the train and the time t of traveling at a constant speed, and find the distance traveled by the train 2 hours after it leaves Beijing.

regular method

The quadratic function model is mainly used to solve practical problems such as maximizing profits and saving materials, etc. It is the focus of the college entrance examination. When solving problems, after establishing the analytical expression of a quadratic function, you can use the collocation method, the discriminant method, the substitution method, the monotonicity of the function, etc. to find the optimal value of the function, thereby solving practical problems.

Track training

The maximum breeding volume of fish in the fishery is m (m>0). In order to ensure the growth space of the fish, the actual breeding volume x is less than m, so as to leave an appropriate amount of free space. It is known that the annual growth of the fish population y is proportional to the product of the actual breeding volume and the idle rate (the idle rate is the ratio of the idle volume to the maximum breeding volume), and the proportional coefficient is k (k>0).

(1) Write the functional relationship expression of y with respect to x, and point out the domain of the function;

(2) Find the maximum annual growth of the fish population.

Power function model

A family makes financial investments. According to the long-term yield market forecast, the income from investing in stable products such as bonds is proportional to the amount of investment, while the income from investing in risky products such as stocks is proportional to the arithmetic square root of the amount of investment. It is known that when investing 10,000 yuan, the income of the two types of products is 1,250 yuan and 5,000 yuan respectively.

(1) Write the functional relationship between the income of the two types of products and the investment amount x;

(2) The family currently has 200,000 yuan of funds, all of which are used for financial investment. Question: How to allocate funds to get the maximum return on investment? How many thousand yuan is the maximum return?

Solution Strategies for Power Function Model Application

(1) Give the functional relational expression containing parameters, use the undetermined coefficient method to find the parameters, and clarify the functional relational expression.

(2) According to the meaning of the question, directly list the corresponding functional relationship expressions.

Function Application PPT, Part 3: Feedback on Compliance

1. Within a certain range, the purchase quantity y of a certain product and the unit price x satisfy a linear functional relationship. If you buy 1,000 tons, the price is 800 yuan per ton, and if you buy 2,000 tons, the price is 700 yuan per ton. Then a customer buys 400 tons, and the price is () per ton.

A． 820 yuanB. 840 yuan

C. 860 yuan D. 880 yuan

2. There are two chain stores of a certain brand of electric vehicles, and their monthly profits (unit: yuan) are y1=-5x2+900x-16 000, y2=300x-2 000, where x is the sales volume. If a total of 110 electric vehicles are sold by two stores in a certain month, the maximum profit is ()

A． 11,000 yuan B. 22,000 yuan

C. 33,000 yuan D． 40,000 yuan

3. A certain mathematics exercise book is priced at 40 yuan. If you purchase more than 9 books at one time, you will receive a discount of 5 yuan for each book and a 10 yuan voucher. If you purchase more than 19 books at a time, you will receive a 10 yuan discount for each book and a 20 yuan voucher. If a class purchases books x (x∈N*, x≤40), the functional relationship between the total cost f(x) and x is ________ (the voucher is equivalent to the equivalent amount).

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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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更新时间: 2024-11-24

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