What are a few real life examples of functions?

The simplest is the proportional function.

For example, if you buy rice, 5 yuan per kilogram, f(x)=5x, the independent variable is the mass of the rice (>=0), and the corresponding variable is the price (》=0).

A little more complicated is the piecewise function:

For example, the water cost of a household is less than 6 tons a month, yuan per ton, 6 tons to 10 tons for the part exceeding six tons, yuan per ton for the part exceeding six tons, etc., the independent variable is the tonnage of water, and the corresponding variable is the water fee.

Another common example is a taxi.

The starting price (within 3 kilometers) is 6 yuan, and what is the price ...... more than 3 kilometersThe independent variable is the mileage, and the variable should be the price.

In special cases, especially when it comes to engineering budgets, more complex functions can be encountered.

Unary linear functions are widely used in our daily life. When people are engaged in buying and selling, especially consumption activities, in social life, if the linear dependence of variables is involved, the unary one-dimensional function can be used to solve the problem.

For example, when we make a purchase, rent a car, or stay in a hotel, the operator often offers us two or more payment options or offers for promotional,** or other purposes. This is when we should think twice and dig deeper into the math in our minds to make an informed choice. As the saying goes:

From Nanjing to Beijing, what is bought is not sold fine. "We must not blindly follow, so as not to fall into the small trap set by the merchant and suffer immediate losses.

Now, I will tell you about one of my personal experiences.

With the diversification of preferential forms, "selective preferential treatment" has gradually been adopted by more and more operators. Once, I went shopping at the "Wumart" supermarket, and an eye-catching sign attracted me, which said that the purchase of teapots and teacups can be discounted, which seems to be rare. What's even stranger is that there are actually two ways to get a discount:

1) Sell one get one free (i.e. buy a teapot and get a teacup free); (2) 10% discount (i.e. payment of 90% of the total purchase price). There are also prerequisites for the purchase of more than 3 teapots (20 yuan for teapots and 5 yuan for teacups).

From this, I can't help but think: is there a difference between the two preferential methods? Which is cheaper?

I naturally thought of functional relations, and I was determined to apply the knowledge of functions I had learned to solve this problem analytically.

I wrote on paper:

Suppose a customer buys x teacups and pays y yuan, (x>3 and x n), then.

Pay y1=4 20+(x-4) 5=5x+60 with the first method;

Pay y2=(20 4+5x) 90%=

Next, compare the relative size of y1y2.

Let d=y1-y2=5x+60-(

Then it's time to discuss:

When d>0, >0, i.e., x>24;

when d=0, x=24;

when d=0, x=24;

To sum up, when there are more than 24 teacups purchased, method (2) saves money; When buying exactly 24 of them, the two methods** are equal; When the number of purchases is between 4 and 23, method (1) is cheaper.

It can be seen that the use of a one-dimensional one-time function to guide shopping not only exercises the mathematical mind, divergent thinking, but also saves money and eliminates waste, which is really a double win!

Real-life application problems.

1. Commodity pricing issues.

Example 1 After the price of a certain brand of color TV is reduced by 30%, the price of each unit is a yuan, then the original price of each color TV of that brand is.

2. The problem of commodity price reduction.

Example 2: The purchase price of a product is 1,000 yuan, and the selling price is 1,500 yuan. Due to the poor sales situation, the store decided to reduce the price**, but to ensure that the profit is 5%, ask the store how much the price should be reduced**.

What are some real-life examples of functions?

Solution: For example, when driving at a constant speed, the distance and time are the functional relations, and the distance speed is time; For example, when boiling water, the power is constant, the amount of boiling water and the time are a function relationship, the more water, the longer it takes to boil; If the total cultivated land area of a village is known, then the per capita cultivated land area is a function of the population, and the per capita area is the total area of the total population.

Therefore, the answer is: the answer is not the only analysis.

Consider the situation in time life where one quantity changes with another, i.e., a function case in life. "Reviews.

Simply put, a function relation is the relationship between a quantity changing with another quantity, and this change is a one-to-one correspondence.

Categories: Education, Science, >> Learning Aid.

Problem description: A real-life function example that illustrates the corresponding definition range and value range.

Analysis: A factory produces a certain product, the ex-factory price of each product is 50 yuan, and its cost is 25 yuan. Because in the production process, on average, there are cubic meters of sewage discharged for each product produced, so in order to purify the environment, the factory designed two plans to treat the sewage and prepare for implementation.

Scheme 1: The factory wastewater is purified and then discharged. The cost of raw materials used for each cubic meter of sewage treatment is 2 yuan, and the monthly loss fee of sewage equipment is 30,000 yuan;

Scheme 2: The factory discharges the sewage to the sewage treatment plant for unified treatment. For every 1 cubic meter treated, a sewage fee of 14 yuan is charged.

Question: 1 Set up a factory to produce x products per month, and the monthly profit is y yuan, and find the functional relationship between y and x when treating sewage according to scheme 1 and scheme 2; (Profit, Total Revenue, Total Expenditure).

2 When setting up a factory with a monthly production capacity of 6,000 products, if you, as the factory manager, should choose which sewage treatment plan should be selected without polluting the environment and saving money, please explain it through calculations.

Solution: (1) Set the selection scheme 1 with a monthly profit of y1 yuan; The monthly profit of option 2 is Y2 yuan.

According to option 1, it is available.

y1＝（50－25）x－2×

25x－x－30000

24x－30000.

y1＝24x－30000.

According to option 2, it is available.

y2＝（50－25）x－14×

25x－7x

18x. y2＝18x.

2) When x 6000, y1 24x 30000 24 6000 30000 114000 (yuan), y2 18x 18 6000 108000 (yuan), y1 y2

It is not enough to form ability by reading books, but more importantly, participating in practice. For example, if you learn to swim alone, you can't learn to swim if you are familiar with books such as "swimming instruction" and listen to the instructor talk about how to ventilate and how to master the movements of the whole body, especially the limbs. You don't have to get off the water, and combined with the guidance, you can really learn to swim in practice.

The research study we are carrying out now is precisely to enable students to form the knowledge and abilities needed for future study and work through various "learning to swim" practices. Through our research work some time ago, the students have basically mastered the methods and means of research problems, if the students are interested, we can also pay attention to other aspects of the things that can be studied, through our research, we deeply realize that there is mathematics around us, mathematics is around, in the future learning process, as long as we have the courage to explore, some students may become real inventors, creators, our current research makes it a foundation, Through our research, we will open up ideas and create good conditions for becoming a mathematician and inventor in the future.

Square area function: s(x)=x, x is the side length, quadratic function.

Conversion of degrees Celsius and Fahrenheit: f(x) = + 32, where x is a function of degrees Celsius.

Resistance = voltage divided by current: r(i) = u i, when the voltage is constant, it is an inverse proportional function.

In the branch of the first quadrant, i>0

Do you mean a metaphor, or a figurative representation of a transaction?