Classical examples of linear function in grade two
Classical mathematics examples 1
1, ]A,, b, is a proportional function c, and there were two points on the image at that time. Among the following judgments, the correct one is D. At that time,
2. In the following statement, []A is incorrect, where Y is proportional to X, and in y=3x+2, Y is proportional to X..
Where s is proportional to x, y is proportional to d when c, xy= 1, and the formula of circular area.
3. The image of linear function y=x+2 is roughly []
A, B, C, D,
4. In the function, the value range of the independent variable X is []
a、x & gt 1 B、x & lt 1C、x？ d、x？ -
5. As shown in the figure, rays OA and OB respectively represent the functional relationship between the distance S traveled by two athletes A and B and the time T, and the speed relationship between them is [].
A, A is faster than B, B is faster than A, C, A and B have the same speed, D is uncertain.
6. If the function value y of the linear function y=(2-m)x-2 decreases with the increase of x, the value range of m is [].
a、m & lt0B、m & gt0C、m & lt2D、m & gt2
7, as shown in figure (1), in Rt△ABC,? ACB=90？ ，D
Is the midpoint of the hypotenuse AB, and the moving point P starts from point B and follows it.
b？ c？ Motion, set, point p motion path
If the process is X, if the function image between Y and X is as shown in Figure (2)
, the area of △ABC is []
a、4 B、6 C、 12 D、 14
8. Miss Li goes to work by bike, at first at a certain speed.
Driving at a constant speed, the bike broke down halfway and was delayed for a few minutes. In order to get to school on time, Miss Li speeded up and kept driving at a constant speed, so she got to school on time. In class, Mr. Li asked the students to draw a schematic diagram of the function image of bicycle driving distance S (kilometers) and driving time T (hours). The schematic diagram drawn by the students is shown in the figure. What you think is right is a, b, c, d,
9. when a. 0, function, y=-|a|x- 1, where the functions in which y decreases with the increase of x are []A, 1 b, 2 c, 3 d, 4.
10. The ground temperature in a certain place is 18℃. If the altitude increases by 1km and the temperature drops by 6℃, the functional relationship between the temperature t(℃) and the altitude h(km) is []A, t= 18-6hB, t =-65438.
1 1, as shown in the figure, is a schematic diagram of an ancient timer "leaky pot". The pot contains a certain amount of water, and the water leaks out from a small hole under the pot. The scale is painted on the wall of the pot, and people calculate the time according to the position of the water surface in the pot. If x is used to represent time and y is the height from the bottom of the pot to the water surface, the following figure is suitable for representing the functional relationship between y and x in a short time (no
A, B, C, D,
12, if the straight line passes through the positive half axis of the y axis, then []
A, n>2 B, n & gt2C, n>, n=2.
13, as shown in the figure: two squares with side lengths of 1 and respectively, one of which is on the same horizontal line, the small square passes through the big square at a uniform speed from left to right along the horizontal line, let the passing time be t, and the area after removing the small square in the big square is s, then the approximate images of s and t should be [].
A, b, c, d, 14, given points M (3 3,2), N( 1,-1), point p is on the y axis, and PM+PN is the shortest, then the coordinates of point p are [] A, (0,) b,.
15. In a cross-country cycling race, the distance Y (km) traveled by two riders at any time is.
The image (whole process) that changes between x (minutes) is shown in the figure. Judging from the image, the following conclusion is incorrect.
[] A, A reaches the finish line B first. In the first 30 minutes, A is in front of B, and C is 48 th.
Minutes, two people meet for the first time. D. the whole journey is 28 kilometers.
Second, fill in the blanks
16. In the proportional function, the proportional coefficient is _ _ _ _ _ _ _ _.
17, known as C=2? R, where c is the _ _ _ _ _ function of R, and the proportional coefficient is _ _ _ _ _.
18, point
19. If the function is on the image of the function, then in a=___. , the range of the independent variable x is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
The value of is 0. 20. When x = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
2 1, in the function, when the value of the independent variable x gradually increases, the value of y gradually _ _ _ _.
And the pumping time t (hours) of the water pump are represented by the following figure. Fill in 22 according to the picture. Residual water in the river.
The following questions:
(1) Before the water was pumped away by the pump, there was _ _ _ _ _ _ water in the river, with the most pumps.
When you can _ _ _ _ _ _ _ _; (2) Pump 8
After that, the remaining water in the river is
________________; (3) When the remaining water in the river is 100, the water pump has pumped away _ _ _ _ _ _ _ _ _.
23, according to the image, determine the analytical formula of the function:
( 1)_______________,(2)____________.
24. A farm plans to plant all vegetables and fruits on 30 mu of open space, and vegetable farmer Xiao Zhang and fruit farmer Xiao Li have contracted the task of planting vegetables and fruits respectively. The function between Xiao Zhang's vegetable planting salary y (yuan) per mu and planting area m (mu) is shown in Figure ①, and the function between Xiao Li's fruit planting reward z (yuan) and planting area n (mu) is shown in Figure ②.
(1) If 20 mu of vegetables are planted, Xiao Zhang's salary for growing vegetables per mu is _ _ _ _ _ _ _ _ _ _ _, and Xiao Zhang's total salary is _ _ _ _ _ _ _ _. At this time, Xiao Li planted _ _ _ _ _ _ mu of fruit, and Xiao Li deserved the reward of _ _. (2) When 10
25. The current output value of a school-run factory is 6.5438+0.5 million yuan. If every additional investment of 654.38+0.000 yuan can increase the output value 250 yuan in one year, then the functional relationship between the total output value Y (ten thousand yuan) and the new investment AMON X (ten thousand yuan) is 26, and the image of the proportional function passes through point A (-654.38+0, -4).
27, function y = k (x-k) (k
28、2,? , 20 12) satisfies the known? 0(i= 1，+？ = 1968, so that the straight line Y = X+I (I = 1, 2,? , 20 12) The probability that an image passes through the first, second and fourth quadrants is _ _ _ _ _ _ _ _ _ _ _ _.
29, known,, then the image through the point and the expression of the function of the point is _ _ _ _ _.
30. A TV station inserted two kinds of advertisements with the length of 20 seconds and 40 seconds in three minutes during prime time one night. The 20-second advertisement costs 6000 yuan each time, and the 40-second advertisement costs 10000 yuan each time. If each advertisement is required to be broadcast at least twice, and the TV station chooses the most profitable broadcast mode, the maximum profit of 3-minute commercial breaks in prime time on this day is _ _ _ _ _ _.
Third, answer questions.
3 1, what value does the function y =(m+2)x-m .( 1)y increase with the increase of x? (2) When m is taken, y decreases with the increase of x?
32. When the value of independent variable x satisfies any condition, the value of function y=5x+ 17 satisfies the following conditions.
( 1)y = 0； (2)y =-7； (3)y=20。
33. The value obtained at the intersection of the image of the known proportional function and the image of the linear function at point P (3, -6). ( 1); (2) If the linear function intersects the X axis at point A, find the coordinates of point A. 。
34. The original length of a spring is 15cm. When the hanging object does not exceed 20kg, the spring will extend by cm for every increase of 1kg. Find the functional relationship between the spring length y(cm) and the suspended object x(kg).
35. A train is traveling at a constant speed of 90km/h, find the functional relationship between its distance s (unit: km) and the traveling time t (unit: hour), and draw the functional diagram.
36.y satisfies the relation 2x-3y+ 1=0. Is y a function of X? ② Is x a function of y? Given two variables x, ask:
If yes, write the relationship between y and x; Explain why.
37. Figure ① is a function image between the balance of payments y (that is, the total fare revenue minus the operating cost) and the passenger volume x of a bus line of a bus company. At present, this line is losing money. In order to turn losses around, the relevant departments held a hearing to raise fares. Passenger representatives think that bus companies should improve management, reduce operating costs and turn losses into profits. The bus company thinks that it is difficult to reduce the operating cost, and the company has tried its best to turn losses.
According to these two opinions, Figure ① can be changed to Figure ② and Figure ③ respectively.
(1) Explain the practical significance of points A and B in Figure ①.
(2) Do you think that in Figure ② and Figure ③, Figure _ _ _ _ _ _ _ reflects the passengers' opinions, and Figure _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(3) If the bus company turns losses into profits by appropriately raising fares and reducing costs, please draw an approximate function image of Y and X in Figure ④.
38. Residents in a city are charged for water by steps. If the monthly water consumption of each household does not exceed 20 tons, it will be charged per ton 1.9 yuan; If the monthly water consumption of each household exceeds 20 tons, the part that does not exceed shall be charged per ton 1.9 yuan, and the part that exceeds shall be charged per ton of 2.8 yuan. Suppose a household consumes x tons of water per month, and the water fee receivable is y yuan. (65,438+0) Write the functional relationship between Y and X when the monthly water consumption does not exceed 20 tons and exceeds 20 tons respectively. (2) If the average water fee of a household in this city is one ton of 2.2 yuan in May, how many tons of water will the household use in May?
39, known. (1) is written as a function of x in the form of y; (2) Write the form that X is a function of Y. 。
40. The distance y (km) and time between Xiaoming and Xiaoying in the school winter cross-country race.
The function image of x (minute) change is shown in the figure. (1) Find the beginning of the game according to the data provided by the picture.
Later, when they first met; (2) According to the information provided by the picture, please design one.
Question, and give the answer.
4 1. The school organizes a summer camp, with an estimated number of people 10 ~ 25. The service quality of the two travel agencies is the same, and the travel expenses are 200 yuan per person. The number of people can be discounted. A travel agency said it can give each passenger a 7.5% discount; Travel agency b said that one tourist can be exempted from the travel expenses, and the rest of the tourists can get a 20% discount. Which travel agency does the school choose with the highest cost performance?
42. Temperature t(℃) and depth H (km) below the rock surface
Changed and changed. The relationship between t and h is approximately a linear function in a certain range.
(2) system. (1) According to the following table, find the functional relationship between t(℃) and h (km);
When the temperature of rock stratum reaches 1770℃, find the depth of rock stratum.
Rice?
43. The post-disaster reconstruction in Wenchuan has been widely concerned by the whole society, and all provinces in China have provided counterpart support to the affected cities and counties in Sichuan Province. Jiange County was aided by our province, and the building materials were transported by train to Hanzhong Railway Station, which is 80 kilometers away from Jiange County/KLOC-0, and then transported by car to Jiange County. A car suddenly broke down on the way to Jiange County. The driver immediately informed the Jiange County Command and immediately checked the maintenance. The Jiange County Command immediately dispatched a second vehicle to meet at 12 minutes after receiving the notice. After emergency repair, the first car was repaired in the eighth minute of the second car's departure and continued to drive at the original speed. Two cars met on the road. In order to ensure the timely delivery of materials, the entourage transferred all materials to the second car (loading and unloading goods)
Ignore the time and U-turn time of B car), B car returns at the original speed and arrives at Jiange County on time as expected. The following figure is a function image between the distance y (km) and the time x (hours) of the A and B cars departing from Jiange County. Please combine the picture information.
Answer the following questions:
(1) Please fill in the data directly in the coordinate system (). (2) Find the resolution function of straight line CD and write the range of independent variables.
(3) Find the speed of car B. 。
44, known function
When x=-3 and y=7. When x=3, find the value of y.
45, e is the midpoint of CD edge, and p is the square of ABCD. As shown in the figure, it is known that the side length of square ABCD is 1.
A moving point on the side, moving point P starts from A, moves forward, and reaches point E. if
The distance traveled by point P is the independent variable X, and the area of △APE is the function Y, so when
How much is it?
Fourth, the application questions
46. Some water in the open-air pool has evaporated (X? 30) After the water, there is still water in the pool. Write the functional relationship between the values of x when y and x, and write the proportional coefficient K.
47. A fruit wholesale market stipulates that when the wholesale price of apples is not less than 100kg, the wholesale price is 2.5 yuan per kilogram. Xiao Wang came to this market with 3000 yuan in cash and bought apples at wholesale price. If the apple he bought is xkg and the remaining cash after Xiao Wang paid is Y yuan, try to write the functional relationship between Y and X, and point out the range of the independent variable X. 。
During May Day, Miss Li organized students to travel to a scenic spot. The admission fee is known to be less than 20 people (including 20 people), and each person is 20 yuan. For those with more than 20 people, the excess is per person 10 yuan. (1) Write down the admission fee Y (yuan) and the number of visitors X (x? 20); (2) Calculate by the relational expression in (1): If Miss Li leads 5 1 students (including 52 teachers) to travel, how much will it cost to buy tickets?
49. A unit urgently needs a car, but it is unable to buy it. The unit leader wants to rent one. The lease condition of a state-owned car rental company is RMB 0/00 per 100 kilometers; The condition of a taxi driver is the monthly salary of 800 yuan, every 100 kilometers 10 yuan. Which car is economical for the unit to rent?
50. After the state implemented the policy of "energy saving and emission reduction, low-carbon economy", an enterprise launched a product named CNG.
According to market research, the cost of the device for converting gasoline into natural gas per vehicle is B yuan:
Fuel cost (including modification cost), (unit: yuan) and normal operation of each vehicle before and after modification.
Time x (unit: day) satisfies the relationships: =ax and =b+50x respectively, as shown in the figure.
(1) The daily fuel cost of each vehicle before modification A = _ _ _ _ _ Try to solve the following problems according to the pictures:
Yuan; The modification fee of each vehicle is B = _ _ _ _ _ _ _ _ _ _ _ Yuan, and after _ _ _ _ _ _ days of normal operation,
The modification cost can be recovered from the saved fuel cost; (2) A taxi company changed it at one time.
100 After the taxi was installed, how many days of normal operation * * * saved 400,000 yuan in fuel costs?
On 5 1, a mobile communication company opened two kinds of communication services. GSM needs to pay 50 yuan fee every month, and the call fee per minute is 0.4 yuan. Shenzhouxing doesn't pay the monthly fee, but it charges 0.6 yuan per minute. A Miao can talk for 200 minutes at most every month. Which service is more suitable for him?
52. A factory has two production lines, A and B, which have been put into production successively. Before production line B was put into production, production line A had produced 200 tons of finished products. Since production line B was put into production, production lines A and B have produced 20 tons and 30 tons every day.
(1) The function expressions of the total output (ton) of A and B and the time (days) since B started production were obtained respectively, and it was pointed out that the total output of A and B was the same by the end of the first few days.
(2) In the rectangular coordinate system, the images of the above two functions are taken as the first quadrant, and the observation images show which production line has high total output at the end of15th and 25th respectively.
53. Xiaogang walked from home to school at 7:30 in the morning. When he passed the Children's Palace, he took 1200 steps, took 10 minutes and arrived at school at 7:55. In order to estimate the distance and other related data, Xiaogang deliberately walked 100 meters on the track and field track of the school at the walking speed of the school. How far is Xiaogang's home from the Children's Palace and how far is the Children's Palace from the school? (2) At 4 o'clock in the afternoon, Xiaogang started from school and walked at a speed of 45 meters per minute. The way home was the same as when he was at school. After playing with his companions for half an hour 300 meters away from the Children's Palace, he quickly went home at a speed of 1 10 meters per minute. Q: ① What time does Xiaogang get home in the afternoon? ② The functional relationship between Xiao Gang's distance S (meters) and time T (minutes) is as shown in the figure. Please write down the coordinates of point B and find the resolution function of the straight line where the line segment CD is located.
Classical Mathematics Example 2
Fill in the blanks (3 points for each small question, * * * 30 points)
(1) point (-3, a) is on the image of linear function y=-2x-6, then a=. (2) The coordinate of the intersection of the linear function y=4-x and the X axis is. If the image of the proportional function passes through y(3) and (4) as shown in the figure, the straight line L is one.
(7) To make a phone call at a public phone booth, you need to pay the phone bill Y (yuan) and the child.
The functional relationship between speaking time x (minutes) is shown in the figure. Xiao Ming needs to pay yuan for playing for 2 minutes; Xiao Li needs to pay 100 yuan to play for 8 minutes.
(8) The image of the linear function passes through the point (-1, 2), and the value of the function y varies with.
If the independent variable x increases or decreases, please write the functional relationship satisfying the above conditions:
Multiple choice questions (3 points for each small question, *** 15 points)
(1) Among the following functions, the one in which y increases with the increase of x is ().
(a) y =-2xb) y =-2x+1(c) y = x-2 (d) y = 2-2x (2) if y? x？ 2? 3b is a proportional function, so the value of b is () a.0b 。
223 C？ d？ 332
(3) Among the four points given below, the one that is not on the straight line y=2x-3 is () A.( 1,-1) B.(0, -3) C. (2, 1)d .( 1).
A. 1.5 m
C.2 meters deep 2.5 meters
(5) the known straight line y=kx+b(k? 0) Intersect the negative half axis with the X axis and the Y axis, and then ()
(A)k & gt； 0，b & gt0(B)k & lt； 0，b & lt0(C)k & gt； 0，b & lt0，(D)k & lt； 0，b & gt0
Three solutions (***55 points) 1, (8 points for this question) In the table below, y is a linear function of X. Complete the table below, write the function expression and draw the function image.
2. (8 points in this question) Draw an image of the straight line y=-2x+2, and answer according to the image: ① Write the intersection of the straight line and the X axis, the coordinates of the intersection with the Y axis ② What is the area of the triangle surrounded by the straight line and the coordinate axis? ③ With the increase of X, how does Y change? 3. (9 points in this question) A city's mobile communication company has opened two kinds of communication services: "Global Connect" pays the monthly fee of 50 yuan first, and then pays the call fee of 0.4 yuan every 1 minute; "Shenzhouxing" doesn't pay the monthly fee, but pays the call fee of 0.6 yuan every 1 minute; (Local calls here), if you talk for x minutes a month, the costs of the two communication methods are y 1 and y2 respectively. ① Write the functional relationship between y 1, y2 and x.
(2) How many minutes a month, the cost of two communication scores is the same.
(3) If someone expects to use 200 yuan within one month, which communication method is more cost-effective? 4. (This question 10) As shown in the figure, lA lB represents the relationship between distance S and time T when A walks on the same road and B rides on the same road. (1)B It's a long way from a 1000 meters (2 minutes) (2). The bike broke down and it took several hours to repair it. (2 points)
(3)B meets A a few hours after departure. (2 points)
(4) Find out the functional relationship between the distance S and the time T that A walks.
(Writing process, 4 points)
5.( 10) Xiao Ming, a clever student, found some interesting phenomena when buying a pair of new sports shoes, that is, there is a certain connection between the number of shoes and the length (cm) of shoes. After collecting data, the following table is obtained:
Please solve the following problems instead of Xiaoming:
(1) Draw corresponding points in the same rectangular coordinate system according to the data in the table. What kind of diagram do you find these points on? (2) Guess what kind of functional relationship between Y and X, find the functional relationship between Y and X, and verify whether the coordinates of these points meet the functional relationship.
(3
) How long are the shoes when the shoe size is 40?
6. (The score of this question is 10) Provide the following information about the linear function: ① It looks like a straight line; ② The straight line passes through three points: (0,0), (1, -a), (a,-4); ③ The independent variable x of the function value increases or decreases.
Based on this information, can you determine the analytical expression of this function? If you can, please write down your idea of solving the problem: if not, what conditions should be added?