a， 1m b， 1.5m c，2m d，2.5m。
8. One day, the central news reported that in order to encourage residents to save water, Beijing will introduce new water standards for residents: ① If the monthly water consumption of each household does not exceed 4 cubic meters, it will be calculated according to the 2 yuan per cubic meter; (2) If the monthly water consumption of each household exceeds 4 cubic meters, the excess shall be calculated as per cubic meter of 4.5 yuan (the excess shall still be calculated as per cubic meter of 2 yuan). Now suppose that a family in this city uses cubic meters of water for a month, and the water fee is RMB, then use images to correctly express the functional relationship with.
9. As shown in the figure, l 1 reflects the relationship between sales revenue and sales volume of a company, and l2 reflects the relationship between sales cost and sales volume of the company's products. When the company is profitable (revenue is greater than cost), the sales volume ().
A is less than 3 tons, B is more than 3 tons, C is less than 4 tons, and D is more than 4 tons.
10. The image in the figure (dotted line ABCDE) describes the functional relationship between the distance s (km) from the starting point and the driving time t (hours) when the car is driving in a straight line. According to the information provided in the picture, the following statements are given: ① The car has traveled * * *120km; ② The car stays for 0.5 hours while driving; ③ The average speed of the car during the whole driving process is km/h; (4) Between 3 hours and 4.5 hours after departure, the vehicle speed gradually decreases. Among them, the correct expression of * * * is ()
a， 1 b，2 c，3 d，4
1 1. A DVD rental store offers two ways to rent discs: one is to rent discs sporadically, each disc is 1 yuan; The other is membership card rental. The card handling fee is per month 12 yuan, and the rental fee is per 0.4 yuan. Xiao Bin often comes to the store to rent discs. If the number of discs rented per month is x,
(1) Write the functional relationship between the payable amount y 1 (yuan) and the number of rental discs x (sheets):
(2) Write the functional relationship between the payable amount y2 (yuan) of the membership card loan method and the number of rented discs X (pieces):
(3) What kind of leasing method is more cost-effective for Xiao Bin?
12. The cost of a product is 10 yuan. The relationship between the sales price of each product X (yuan) and the daily sales volume Y (pieces) in the trial sales stage is as follows:
X (yuan) 15 20 30 …
Y (piece) 25 2010 ...
If the daily sales volume Y is a linear function of the sales price X 。
(1) Find the functional relationship between daily sales y (pieces) and sales price x (yuan):
(2) How much should the sales price of each product be set to maximize the daily sales profit? What is the daily sales profit at this time?
13, figure 9 shows the distance S(km) and time t(min) traveled by the car.
Function diagram of. Observe the information provided in the diagram and answer the following questions:
(1) The average speed in the first 9 minutes is
How long did the bus stop on the road?
(3) When 16≤t≤30, find the functional relationship between S and T. 。
14, as shown in figures 15- 1 and 15-2, in a 20×20 equidistant grid (the width and height of each grid are 1 unit length), Rt△ABC starts from the position where point A coincides with point M, every second.
(1) as shown in figure 15- 1, when Rt△ABC moves down to the position of rt △ a1b1,please draw rt △ a1b in the grid.
(2) As shown in Figure 15-2, during the downward translation of Rt△ABC, please find out the functional relationship between Y and X, and explain how the maximum and minimum values of Y are obtained when taking X respectively. What are the maximum and minimum values respectively?
(3) During the translation of RT △ ABC to the right, please explain what value X takes and what value Y takes to get the maximum and minimum values. What is the maximum value and the maximum value respectively? Why?
15. In a certain place, it is found that the relationship between the number of times a cricket calls 1 min and the local temperature is approximately a linear function. The following is a comparison table between the number of crickets and the temperature change:
Cricket's cry … 84 98 1 19 …
Temperature (℃) … 15 17 20 …
(1) Determine the relationship of linear functions according to the data in the table;
(2) If the cricket croaked 63 times in 1 minute, what was the temperature at that time?
16. There are two charging methods for dialing into the network in a certain place, and users can choose one of them:
(1) Timing system: 0.05 yuan/minute; (2) Monthly subscription system: 50 yuan/month (limited to one personal home phone).
In addition, there is a communication fee of 0.02 yuan/minute for each online mode.
(1) Please write down the functional relationship between user's monthly fee y (yuan) and online time x (hours) under two charging methods: time system: monthly system:
(2) If a user estimates that the online time is 20 hours a month, which way do you think is more cost-effective?
17. The personal monthly income of the marketing staff in the marketing department of a company has a functional relationship with the monthly sales volume of the marketing staff. The image is as shown in the figure. According to the information provided in the picture, answer the following questions:
(1) Find the functional relationship between a marketer's personal monthly income of Y yuan and the marketer's monthly sales of X million pieces (x≥0):
(2) It is known that Li Ping, a salesman of this company, sold 6.5438+0.2 million pieces in May to seek Li Ping's income in May.
18, the distance from Ning 'an to Harbin is 360 kilometers. A car is in Ning 'an and B car is in Harbin. The two cars set out at the same time, facing each other and meeting at location A. In order to save money (after the two cars meet to exchange goods, they must return to the starting point by the same route), after the two cars exchange goods, car A immediately returns to Ning 'an by the same route. Assume that the speed of each car remains constant during driving.
(1) Speed of vehicle A: Speed of vehicle B:;
(2) Explain the movement state of B car from two cars to five hours.
19. A company went to the orchard base to buy some high-quality fruits to express condolences to medical workers. Orchard base has two sales plans for those who buy more than 3000 kg (including 3000 kg). Scheme A: Each kilogram of 9 yuan is delivered to the door from the base. Scheme B: Each kilogram of 8 yuan will be transported back by the customer by car. It is known that the transportation fee for renting a car from the base to the company is 5000 yuan.
(1) Write down the functional relationship between the payment (yuan) of the company's two procurement schemes and the quality (kg) of the fruits purchased, and write down the range of independent variables.
(2) According to the purchase quantity, which purchase scheme pays the least? And explain why.
20. As shown in the figure, in the rectangular OABC, O is the origin of the rectangular coordinate system, and the coordinates of point A and point C are (3,0) and (0,5) respectively.
(1) Write the coordinates of point B directly;
(2) If the straight line CD passing through point C intersects with the AB side of point D, and the circumference of the rectangular OABC is divided into two parts: 1∶3, then the analytical expression of the straight line CD is obtained;
2 1. Please read the following paragraphs before answering the questions.
There is such a narrative in the junior high school mathematics textbook: "Comparing the sizes of A and B, we can first find the difference between A and B, and then see if the difference is positive, negative or zero." It can be seen that to judge the values of two algebraic expressions, we only need to examine their differences.
Question: Party A and Party B buy grain twice in the same grain store at the same time (assuming that the unit price of the grain purchased twice is different). Every time Party A buys grain 100 kg, Party B spends 100 yuan each time.
Suppose that the unit price of grain purchased by Party A and Party B for the first time is X yuan per kilogram, and the unit price of grain purchased for the second time is Y yuan.
(1). Represented by an algebraic expression containing X, Y: A needs to pay RMB * * * to buy grain twice; Party B bought 100 kg of grain twice. If the average unit price of grain purchased twice by Party A is Q 1 yuan per kilogram and the average unit price of grain purchased twice by Party B is Q2 yuan per kilogram, then Q 1=, Q2=.
(2) If it is stipulated that whoever buys grain twice has a low average price, then the way of buying grain is more cost-effective. Please judge which way is more cost-effective for Party A and Party B to buy grain, and explain the reasons.
22. There are two charging standards for mobile phone charges of a communication company, A and B, as shown in the following table:
Remarks on monthly fee (yuan/department) and communication fee (yuan/minute)
One charging standard is 50 0.4. If the call time is less than 1 minute, it will be calculated as 1 minute.
B charging standard 0 0.6
Suppose a user's cell phone talk time is x minutes a month. Please answer the following questions according to the above table: (1) According to Class A charging standard, users should pay y 1= yuan; According to the charging standard of Class B, users should pay y 1= yuan; (expressed by an algebraic expression with X) (2) If the user's monthly call time is 300 minutes, which billing method should he choose? (3) If the user's monthly mobile phone fee does not exceed 90 yuan, which billing method should he choose?
23. Someone started from City A and went to City B, 30 kilometers away from City A. Now there are three kinds of cars for him to choose from: ① Bicycle, speed15 km/h; ② Tricycle with speed 10 km/h; (3) a motorcycle with a speed of 40km/h. ..
(1) Which buses can get him from City A to City B within 2 hours? Please explain the reason.
(2) Assuming that this person is s kilometers away from the city B on the way, and the travel time is short, try to write the functional relationship between the selected scheme S and T (1) (indicate the range of independent variable T):
(3) Draw the image of this function in the plane rectangular coordinate system given in Figure 7.
24, a company to the orchard base to buy some kind of high-quality fruit condolences to medical workers, orchard base to buy more than 3000 kg (including 3000 kg), there are two sales procedures. Scheme A: Each kilogram of 9 yuan is delivered to the door from the base. Scheme B: Each kilogram of 8 yuan is transported back by the customer by car. It is understood that the transportation fee for renting a car from the base to the company is 5000 yuan.
(1) Write the functional relationship between the payment for goods y (yuan) and the fruit quantity x (kg) of the two purchasing schemes of the company respectively, and write the range of the independent variable x..
Option a:
Option b:
(2) When the purchase amount is in what range, which purchase scheme should be chosen to pay the least? And explain why.
25. As we all know, the relationship between the average temperature and altitude in mountainous areas is shown in the following table:
Altitude (m) 0 100 200 300 400 ...
Average temperature (unit "℃) 22 265 438+0.5 265 438+0 20.5 20 ...
(1) If the altitude is expressed in (meters) and the average temperature is expressed in (℃), try to write the functional relationship between and;
(2) If a plant is suitable for growing in mountainous areas with an altitude of 18℃ ~ 20℃ (including 18℃ and 20℃), what is its suitable altitude for planting?
26. The ex-factory price of each product produced by a textile factory was originally 80 yuan, and the cost was 60 yuan. Because every product is produced in the production process, an average of 0.5m3 of sewage is discharged. In order to protect the environment, the sewage must be purified before being discharged. It is known that the cost of treating 1 m3 sewage is 2 yuan, and the monthly loss of sewage treatment equipment is 8,000 yuan. Now the factory produces X products every month, with a monthly net profit of Y yuan:
(1) Find the functional relationship between Y and X, (net profit = total income-total expenditure)
(2) When y= 106000, find the number of products produced by this factory this month.
27. Through market survey, there is the following functional relationship between the demand y (kg) for characteristic agricultural products in a certain area and the market price x (yuan/kg): y = (0
(1) According to the above market survey, please analyze the market price of this agricultural product in this area and the total sales income of farmers in this period when the market is in a balanced state.
(2) With the support of the national policy of "agriculture, countryside and farmers", farmers in this area use high and new technology to transform traditional production methods, reduce output and greatly improve product quality. At this time, the functional relationship between production quantity Z and market price X has changed, while the functional relationship between demand has not changed. When the market reaches equilibrium again, the market price rises by a (0
28. (1) When the A tractor started to work, there was 30 liters of oil in the fuel tank. If the fuel consumption is 6 liters/hour, find the functional relationship between the remaining fuel quantity y (liter) and the working time x (hour).
(2) As shown in the figure, line AB represents the functional relationship between the remaining oil quantity y (liter) in the fuel tank of B brand tractor and the working time x (hour). If the price, quality, performance and after-sales service of brand A and brand B tractors are the same, according to the information provided in the picture, which brand of tractor would you like to buy and explain the reasons?
29, 4× 100 meter rally is one of the most exciting events in the school sports meeting. Are the solid line and dotted line in figure 10 three levels respectively? Class one, grade three? The function image of the distance y (meters) run by athletes and the time x (seconds) spent by the team during the competition (assuming that the running speed of each athlete is constant, ignoring the time of handing the bat).
Question:
(1) Grade three? The fastest runner in Class Two is a _ _ _ _ great runner;
(2) How long did it take for the athletes of the two classes to draw for the first time after the game started?