First, multiple-choice questions:
1. It is known that Y is proportional to x+3. When x= 1 and y=8, the functional relationship between Y and X is ().
(A)y = 8x(B)y = 2x+6(C)y = 8x+6(D)y = 5x+3
2. If the straight line y=kx+b passes through the first, second and fourth quadrants, then the straight line y=bx+k does not pass through ().
(a) One quadrant (b) Two quadrants (c) Three quadrants (d) Four quadrants
3. The area of the triangle surrounded by the straight line y=-2x+4 and the two coordinate axes is ().
(A)4 (B)6 (C)8 (D) 16
4. If the resolution function between the length y(cm) of two springs A and B and the mass x(kg) of the suspended object is y=k 1x+a 1 and y=k2x+a2 respectively, as shown in the figure, when the mass of the suspended object is 2kg, the length of spring A is y 1.
(A)y 1 >y2 (B)y 1=y2
y 1 & lt； Y2 (D) cannot be determined.
5. Set b>a, draw the images of functions y=bx+a and y=ax+b once in the same plane rectangular coordinate system, and then there will be a set of values of A and B, so that one of the following four diagrams is correct ().
6. If the straight line y=kx+b passes through the first, second and fourth quadrants, then the straight line y=bx+k does not pass through the () quadrant.
One (b) two (c) three (d) four
7. The linear function y=kx+2 passes through the point (1, 1), so this linear function ().
(A)y increases with the increase of x (B)y decreases with the increase of x.
(c) The image passes through the origin (d), and the image does not pass through the second quadrant.
8. No matter why m is a real number, the intersection of straight lines y=x+2m and y=-x+4 cannot be in ().
(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant
9. To get the image of y=- x-4, you can put the straight line y=- x ().
(a) translation by 4 units to the left, and (b) translation by 4 units to the right.
(c) translate 4 units up; (d) translate 4 units down.
10. If the function y=(m-5)x+(4m+ 1)x2(m is a constant) is proportional to x, then the value of m is ().
(A)m & gt； -(B)m & gt； 5 (C)m=- (D)m=5
1 1. If the intersection of the straight line y=3x- 1 and y=x-k is in the fourth quadrant, then the range of k is ().
(A)k & lt； (B)& lt； k & lt 1(C)k & gt； 1(D)k & gt； 1 or k
12. A straight line passing through point P (- 1, 3) makes it the triangle area surrounded by two coordinate axes 5, so that a straight line can be used as ().
Articles 4 (b), 3 (c), 2 (d), 65-438 +0
13. Given abc≠0 and =p, then the straight line y=px+p must pass ().
(a) first and second quadrants, (b) second and third quadrants.
(c) the third and fourth quadrants (d) the first and fourth quadrants
14. when-1≤x≤2, the function y=ax+6 satisfies y < 10, and the value range of constant a is ().
(A)-4 & lt； a & lt0(B)0 & lt； a & lt2
(C)-4 & lt； A<2 and a = 0 (d)-4
15. In the rectangular coordinate system, A( 1, 1) is known, and the point p is determined on the X axis so that △AOP is an isosceles triangle, then the qualified point P*** has ().
1 (B)2 (C)3 (D)4。
16. the image of the linear function y=ax+b(a is an integer) passes through the point (98, 19), the x axis crosses (p, 0), and the y axis crosses (0, q). If p is a prime number and q is a positive integer, then the number of linear functions that meet the conditions is ().
(A)0 (B) 1 (C)2 (D) countless.
17. In the rectangular coordinate system, the point whose abscissa is all integers is called the whole point, and k is an integer. When the intersection of the straight line y=x-3 and y=kx+k is the whole point, the value of k can be taken as ().
2 (B)4 (C)6 (D)8
18. In the rectangular coordinate system, the point whose abscissa is an integer is called the whole point, and let k be an integer. When the intersection of straight lines y=x-3 and y=kx+k is the whole point, the value of k can be taken as ().
2 (B)4 (C)6 (D)8
19. Party A and Party B run back and forth on the slope AB as shown in the figure. It is known that Party A's uphill speed is 1m/min and downhill speed is 2m/min, (A
20. If k and b are two real roots (kb≠0) of the unary quadratic equation x2+px-│q│=0, in the linear function y=kx+b, y decreases with the increase of x, then the image of the linear function must pass ().
(a) Quadrant 1, 2 and 4 (b) Quadrant 1, 2 and 3.
(c) Quadrants 2, 3 and 4 (D) Quadrants 1, 3 and 4.
Second, fill in the blanks
1. The known linear function y=-6x+ 1. When -3≤x≤ 1, the value range of y is _ _ _ _ _ _ _.
2. It is known that the image with linear function y=(m-2)x+m-3 passes through the first, third and fourth quadrants, so the value range of m is _ _ _ _ _ _.
3. The image of a function passes through the point (-1, 2), and the value of function y decreases with the increase of x, please write the function relation that satisfies the above conditions: _ _ _ _ _ _ _ _.
4. It is known that the straight line y=-2x+m does not pass through the third quadrant, so the value range of m is _ _ _ _ _ _ _.
5. There is a point P on the image of function y=-3x+2, so that the distance from P to X axis is equal to 3, and the coordinate of point P is _ _ _ _ _ _ _ _.
6. The primary resolution function passing through point P (8 8,2) and parallel to the straight line y=x+ 1 is _ _ _ _ _ _ _.
7. Images with 7.y = x and y=-2x+3 intersect in the _ _ _ _ _ _ _ quadrant.
8. A company stipulates that retired employees can get a pension every year, and the amount is directly proportional to the arithmetic square root of working years. If he works for one more year, his pension will be P yuan more than before, and if he works for two more years (b≠a), his pension will be Q yuan more than before, so his annual pension will be _ _ _ _.
9. If the linear function y=kx+b, when -3≤x≤ 1, the corresponding y value is 1≤y≤9, then the analytical formula of the linear function is _ _ _ _ _ _.
10. (2005 Junior High School Mathematics Competition in Nanxun District, Huzhou City) Let the area of the graph enclosed by a straight line KX+(k+ 1) Y- 1 (positive integer) and two coordinates be Sk(k= 1, 2,3, ...
1 1. According to relevant statistics, there is a T= relationship (k is a constant) between the number of telephone calls t between two cities every day and the population m, n (unit: 10,000 people) and the distance d (unit: km) between the two cities. At present, the population and the distance between the populations of cities A, B and C are calculated as shown in the figure.
Third, answer questions.
1. It is known that the image of linear function y=ax+b passes through points A (2 2,0) and B (0 0,4). (1) Find the analytical expression of the linear function and draw the image of the function in the rectangular coordinate system; (2) If the value of function y in (1) is in the range of -4≤y≤4, what range is the corresponding value of y?
2. It is known that y=p+z, where p is a constant, z is proportional to x, and when x=2, y =1; When x=3, y =- 1.
(1) Write the functional relationship between y and x;
(2) If the range of x is 1≤x≤4, find the range of y. 。
3. For the sake of students' health, the heights of desks and stools in schools are scientifically designed according to a certain relationship. Xiao Ming observed and studied a batch of desks and stools bought by the school and found that they can adjust their height according to people's height. So he measured the four heights corresponding to a set of tables and chairs and got the following data:
first gear
second gear
third gear
Fourth gear
Step height x (cm)
37.0
40.0
42.0
45.0
Table height y (cm)
70.0
74.8
78.0
82.8
(1) After exploring the data, Xiao Ming found that the table height y is a linear function of the stool height x, please find out the relationship of this linear function; (the range of x is not required); (2) After Xiao Ming came home, he measured the desk and stool at home. The height of the desk is 77cm and the height of the stool is 43.5cm. Would you please judge whether they match? Explain why.
Xiaoming went for a spring outing in the suburbs by bike. The following figure is a function image of the relationship between the distance from home y (kilometers) and the time spent x (hours). (1) According to the image, how many hours does it take Xiao Ming to get to the farthest place from home? How far is it from home at this time? (2) Xiaoming left home for two and a half hours. How far is it from home? (3) How long has Xiao Ming been away from home? 12km？
5. Given the image of linear function, the X axis is at a (-6,0), the image of orthogonal proportional function is at point B, and point B is in the third quadrant. Its abscissa is -2, and the area of delta △AOB is 6 square units. Find the analytic expressions of orthogonal proportional function and linear function.
6. As shown in the figure, a beam of light starts from point A (0, 1) on the Y axis, reflects at point C on the X axis, and then passes through point B (3, 3) to find the path length of light from point A to point B. 。
7. Equation │ X-1│ Y-1│ =1What is the figure enclosed by the curve and what is its area?
8. In the cartesian coordinate system x0y, the image of the linear function y= x+ intersects the X axis and the Y axis at points A and B respectively. The coordinate of point C is (1, 0), point D is on the X axis, and ∠BCD=∠ABD. Find the analytical formula of the linear function of the image passing through point B and point D.
9. For the image with known linear function y= x-3, the X-axis and Y-axis intersect at point A and point B respectively, the vertical line passing through point C (4,0) is AB intersecting at point E, and the Y-axis intersecting at point D, thus the coordinates of point D and point E can be obtained.
10. It is known that the intersection of the straight line y= x+4 with the X axis and Y axis is A and B respectively, and the coordinates of P and Q are P (0,-1) and Q(0, k) respectively, where 0.
1 1.(2005 Jiaochuan Cup Junior Two Mathematics Competition in Ningbo) A leasing company * * * has 50 combine harvesters, including 20 A and 30 B. Now these 50 combine harvesters are sent to A and B to harvest wheat, including 30 A and 20 B, and the daily rental price agreed between the two places and the leasing company.
Harvester rent
B harvester rent
Adidas
1800 yuan/set
1600 yuan/set
B di
1600 yuan/set
1200 yuan/set
(1) Set up X combine harvesters and send them to a certain place, and the rental company will pay Y (Yuan) per day for these 50 combine harvesters. Please use X for Y and indicate the range of X. 。
(2) If the total rent of 50 combine harvesters of the leasing company is not less than 79,600 yuan a day, explain how many distribution schemes there are and write out various schemes.
12. It is understood that the tax calculation method of remuneration for writing articles and publishing books is as follows
F(x)= where f (x) means that the contribution fee is X yuan, which is the taxable amount. If Zhang San gets the manuscript fee and pays personal income tax, he gets 7 104 yuan. How much is Zhang San's manuscript fee?
13. A middle school is expected to spend 1500 yuan to buy X commodity A and Y commodity B, but the price of each commodity A rises 1.5 yuan, and the price of each commodity B rises 1 yuan. Although the quantity of goods purchased by A decreased by 10, the total amount was mostly 29 yuan. If each commodity A only increases by 1 yuan,
(1) Find the relationship between x and y;
(2) If the sum of twice the quantity of goods expected to buy A and the quantity of goods expected to buy B is greater than 205, but less than 2 10, find the values of X and Y. 。
14. In order to save water, a city stipulates that when the monthly water consumption of each household does not exceed the minimum am3, only the basic fee 8 yuan and the fixed loss fee C yuan (C ≤ 5) are paid; If the water consumption exceeds am3, in addition to the above-mentioned basic expenses and loss expenses, an excess fee of B yuan shall be paid per kloc-0/m3.
The water consumption and payment expenditure of a family in a city this year 1 month, February and March are shown in the following table:
Water consumption (cubic meters)
Pay water fee (yuan)
January
nine
nine
February
15
19
March
22
33
Find a, b and c according to the data in the above table.
15.A, B and C have 10, 10 and 8 machines, and it is decided to support these machines to 18 in D and 10 in E. It is known that the freight for transporting a machine from A to D and E is 200 yuan and 800 yuan respectively. Transport a machine from B city to D city and E city, and the freight is 300 yuan and 700 yuan; The freight charges for transporting a machine from C to D and E are 400 yuan and 500 yuan respectively.
(1) Let's transfer X units from City A and City B to City D. When transferring 28 machines, find the functional relationship between total freight W (yuan) and X (units), and find the maximum and minimum value of W. 。
(2) Assume that Station X is transferred from City A to City D and Station Y is transferred from City B to City D.. When 28 machines are scheduled, the total freight w (yuan) is represented by x and y, and the maximum and minimum values of w are found.
Answer:
1.B 2。 B 3。 A 4。 A
5.b Tip: From the solution of the equations, the intersection of two straight lines is (1, a+b).
The abscissa of the intersection point in Figure A is negative, so Figure A is wrong; The abscissa of that intersection in figure c is 2≠ 1,
Therefore, Figure C is incorrect; The ordinate of the intersection in figure d is a number greater than a and less than b, which is not equal to a+b,
Therefore, Figure D is incorrect; So choose B.
6.b prompt: ∫ straight line y=kx+b passes through the first, second and fourth quadrants, ∴ for straight line y = bx+k.
The image does not pass through the second quadrant, so you should choose B.
7.b prompt: ∫y = kx+2 passes (1, 1), ∴ 1=k+2, ∴y=-x+2.
∫k =- 1 & lt； 0, ∴y decreases with the increase of x, so b is correct.
∵y=-x+2 is not a proportional function, and its image does not pass through the origin, so c is wrong.
∵k & lt； 0，b = > 2 & gt； 0, ∴ Its image passes through the second quadrant, so d is wrong.
8.c9.d hint: According to the image relationship of y=kx+b,
Translate the image with Y =-X down by 4 units to get the image with y=- x-4.
10.c tip: ∫ function y=(m-5)x+(4m+ 1)x, where y is proportional to x,
∴ ∴m=-, so c
11.b12.c13.b Hint: ∵ =p,
∴ ① If a+b+c≠0, then p = = 2；;
② if a+b+c=0, then p= =- 1,
∴ When p=2, y=px+q passes through the first, second and third quadrants;
When p=- 1, y=px+p passes through the second, third and fourth quadrants.
To sum up, y=px+p must pass through the second quadrant and the third quadrant.
14.D 15。 D 16。 A 17。 C 18。 C 19。 C
20. A hint: according to the meaning of the question, △ = P2+4 │ Q │ > 0，k b & lt0,
In the linear function y=kx+b, y decreases with the increase of x, and the image of the linear function must pass through the first, second and fourth quadrants. Choose one.
Second,
1.-5≤y≤ 19 2.2 & lt； M<3 3. For example, y=-x+ 1 etc.
4.M ≥ 0。 Tip: The possible situations of images with y=-2x+m should be considered comprehensively.
5. (,3) or (,-3). Tip: ∵ The distance from point P to X axis is equal to 3, and the ordinate of point P is 3 or -3.
When y=3, x =；; When y=-3, x =；; ∴ The coordinate of point P is (,3) or (,-3).
Tip: "The distance from point P to X axis is equal to 3" means that the absolute value of the ordinate of point P is 3, so the ordinate of point P should be in two cases.
6.y = x-6。 Tip: Let the analytical expression of linear function be y = kx+b. 。
The line y=kx+b is parallel to y=x+ 1, and k =1
∴ y = x+B. If p (8 8,2) is replaced, 2=8+b, and b=-6. The analytical formula of ∴ is y = x-6.
7. Solving equations
The coordinate of the intersection of two functions is (,), which is in the first quadrant.
8.9.y = 2x+7 or y =-2x+3 10.
1 1. According to the meaning of the question, there are t= k, ∴ k = t.
So, the daily telephone number between B city and C city is T? BC=k×。
Third,
1.( 1) From the meaning of the question:
∴ The analytic formula of this unary function is: y =-2x+4 (function image is abbreviated).
(2)∫y =-2x+4，-4≤y≤4，
∴-4≤-2x+4≤4,∴0≤x≤4.
2.( 1) ∵ z is proportional to x, ∴ let z=kx(k≠0) be a constant.
Then y = p+kx. x=2，y = 1； X=3, y=- 1 substitute y=p+kx respectively.
The solution is k=-2, p=5,
The functional relationship between y and x is y =-2x+5;
(2)∵ 1≤x≤4。 Substitute x 1= 1 and x2=4 into y=-2x+5, respectively, and get y 1=3 and Y2 =-3.
1≤x≤4, -3 ≤ y ≤ 3.
Another solution: ∫ 1≤x≤4, ∴-8≤-2x≤-2, -3≤-2x+5≤3, that is, -3 ≤ y ≤ 3.
3.( 1) Let the linear function be y=kx+b and take any data in the table.
Do not substitute (37.0, 70.0) and (42.0, 78.0), and get
The linear function relation is y = 1.6x+ 10.8.
(2) When x=43.5, y =1.6× 43.5+10.8 = 80.4. ∵ 77 ≠ 80.4, ∴ Mismatch.
4.( 1) According to the picture, it takes Xiaoming 3 hours to get to the farthest place from home. At this time, he was 30 kilometers away from home.
(2) Let the analytical formula of linear CD be y=k 1x+b 1, which is represented by c (2, 15), d (3, 30),
Substitution: y= 15x- 15, (2 ≤ x ≤ 3).
When x=2.5, y=22.5 (km)
A: Two and a half hours after departure, Xiao Ming left home for 22.5 kilometers.
(3) Let the analytical formula of the straight line passing through e and f be y=k2x+b2,
Substitute e E (4 4,30) and F (6 6,0) into y=- 15x+90, (4≤x≤6).
The analytical formula of the straight line passing through point A and point B is y=k3x,
∵b( 1, 15),∴y= 15x.(0≤x≤ 1)，
Let y= 12, x= (hours) and x= (hours) respectively.
A: Xiaoming left home in hours or hours12km.
5. let the proportional function y=kx and the linear function y=ax+b,
∵ Point B is in the third quadrant, and the abscissa is -2. Let B(-2, yB), where Yb
∵S△AOB=6,∴ AO │yB│=6，
∴yB=-2. Substitute point B (-2, -2) into the proportional function y=kx to get k = 1.
Substitute points a (-6,0) and b (-2,2) into y=ax+b, and you get
Y = x, y=- x-3 is what you want.
6. Extend the X-axis of BC to D, making it DE⊥y-axis and BE⊥x-axis, and submit it to E. Prove △ AOC △ Doc.
∴od=oa= 1,ca=cd,∴ca+cb=db= = 5。
7. When x≥ 1 and y≥ 1, y =-x+3; When x≥ 1, y
When x
Therefore, the figure surrounded by the curve is a square with a side length of and an area of 2.
8.∵ Points A and B are the intersections of straight line y= x+ with X axis and Y axis respectively.
∴A(-3,0),B(0，)，
The coordinate (1, 0) of point ∫ C is given by Pythagorean theorem BC=, AB=,
The coordinate of point d is (x, 0).
(1) When point D is on the right side of point C, that is, X >；; 1,
∵∠bcd=∠abd,∠bdc=∠adb,∴△bcd∽△abd，
∴ ,∴ ①
∴ ,∴8x2-22x+5=0，
∴x 1=, x2=, tested: x 1=, x2=, which is the root of equation ①,
∫x =, it doesn't matter, ∴ give up, ∴x=, ∴ d point coordinates are (,0).
Let the main resolution function of the image passing through point B and point D be y=kx+b,
∴ Found that the linear function is y =-x+.
(2) If point D is to the left of point C, then X
∴ ,∴ ②
∴8x2- 18x-5=0, ∴x 1=-, x2=, which is the root of equation ②.
X2 = irrelevant, ∴x 1=-, ∴D point coordinates are (-,0),
∴ The main resolution function of the image passing through two points B and D(-, 0) is y=4 x+,
To sum up, the linear function satisfying the meaning of the question is y=- x+ or y = 4x+.
9. The straight line y= x-3 intersects the X axis at point A (6 6,0) and the Y axis at point B (0 0,3).
∴oa=6,ob=3,∵oa⊥ob,cd⊥ab,∴∠odc=∠oab，
That is ∴cot∠ODC=cot∠OAB,
∴ OD = = 8。 The coordinate of point d is (0,8),
Let the linear analytical formula of CD be y=kx+8, and substitute c (4 4,0) into 0=4k+8 to get k =-2.
∴ straight CD: y =-2x+8, by
∴ The coordinates of point E are (,-).
10. Substitute x=0 and y=0 into y= x+4 respectively.
∴ The coordinates of point A and point B are (-3,0) and (0,4) respectively.
oa = 3，OB=4，∴AB=5，BQ=4-k，QP = K+ 1。 When QQ'⊥AB is in q' (as shown),
When QQ ′ = qp, ⊙Q is tangent to the straight line AB. From RT△bqq'∽RT△Bao, we get.
. ∴ ,∴k=。
When k=, q is tangent to the straight line AB.
1 1.( 1)y=200x+74000， 10≤x≤30
(2) Three schemes, the sequence is x=28, 29, 30.
12. let the contribution fee be x yuan, ∫ x > 7 104 >400,
∴x-f(x)=x-x( 1-20%)20%( 1-30%)=x-x x = x = 7 104。
∴x=7 104× =8000 (yuan). A: This manuscript fee is 8,000 yuan.
13.( 1) Assume that the estimated unit prices of goods A and B are RMB A and RMB B respectively.
Then the original plan is: ax+by= 1500, ①.
When the unit price of commodity A increases by 1.5 yuan, that of commodity B increases by 1 yuan and that of commodity A decreases by 10, we get: (a+1.5) (x-10)+(b+/kloc).
Then, if the unit price of a commodity rises by 1 yuan, and the quantity is five less than expected, the unit price of b commodity still rises by 1 yuan: (a+1) (x-5)+(b+1) y =1563.5.
From ①, ②, ③: ④-⑤×2, the result is x+2y = 186.
According to the meaning of the question: 205
Because y is an integer, y=55 and x = 76.
14. suppose that the monthly water consumption is xm3 and the water fee is y yuan, then y=
Judging from the meaning of the question: 0
Therefore, the water consumption of 15m3 and 22m3 is greater than the minimum limit am3.
Substitute x= 15 and x=22 into equation ②, and get the solution of b=2, 2a=c+ 19, ⑤.
Then analyze whether the water consumption in January exceeds the minimum limit, and set 9>,
Substituting x=9 into ② gives 9=8+2(9-a)+c, that is, 2a=c+ 17, ⑥.
⑤ contradiction ⑤ Therefore, if 9≤a, the payment method in January should be ①, then 8+c=9.
∴c= 1 Substitute into formula ⑤, and a = 10.
To sum up, a= 10, b=2, C = 1. ()
15.( 1) As mentioned above, the number of machines sent from city A, city B and city C to city D is x, x, 18-2x.
The number of machines sent to E city is 10-x, 10-x and 2x- 10 respectively.
So w = 200x+300x+400 (18-2x)+800 (10-x)+700 (10-x)+500 (2x-10) =
and
∴5≤x≤9, ∴W=-800x+ 17200(5≤x≤9, x is an integer).
As can be seen from the above formula, w decreases with the increase of x,
So when x=9, w takes the minimum value 10000 yuan;
When x=5, w reaches the maximum value 13200 yuan.
(2) According to the topic, the number of machines sent from city A, city B and city C to city D is x, y, 18-x-y respectively.
The number of machines sent to E city is 10-x, 10-y, x+y- 10 respectively.
So w = 200 x+800 (10-x)+300 y+700 (10-y)+400 (19-x-y)+500 (x+y-/kloc-0).
=-500x-300y- 17200。
and
∴W=-500x-300y+ 17200 and (x, y is an integer).
w =-200 x-300(x+y)+ 17200 ≥- 200× 10-300× 18+ 17200 = 9800。
When x = 10 and y=8, W = 9800. So the minimum value of w is 9800.
w =-200 x-300(x+y)+ 17200 ≤- 200 x 0-300 x 10+ 17200 = 14200。
When x=0, y= 10, W= 14200,
So the maximum value of w is 14200.
The senior high school entrance examination always reviews the function once.
Fill in the blanks
1. In the function y=, the value range of the independent variable x is _ _ _ _ _ _ _ _ _ _ _ _.
Answer: x≠4
Tip: To make the score meaningful, the denominator is not equal to 0, that is, x-4≠0.
2. linear function y=kx+b, when k
Answer: Reduce
Hint: According to the properties of linear function, when k < 0, y decreases with the increase of x 。
3. If the image of the proportional function passes through point (2, -3), its image passes through quadrant _ _ _ _ _ _ _.
Answer: Two, four.
Hint: k =-< 0, y decreases with the increase of x, passing through the origin and the second and fourth quadrants.
4. If the image of function y=kx- 1 passes through this point (-1, 5), then the value of k is _ _ _ _ _ _ _ _ _ _ _ _.
Answer: -6
Tip: When the image passes through the point (-1, 5), that is, x=- 1, y=5 is substituted.
5. In △ ABC, ∠B=∠A=α, then the relationship between ∠C and α is _ _ _ _ _ _ _.
Answer: ∠ c = 180-2α.
Hint: the theorem of sum of interior angles of triangle.
6.(20 10 Heilongjiang senior high school entrance examination) Point A is a point on the straight line y=-2x+2, and the distance from point A to the two coordinate axes is equal, so the coordinate of point A is _ _ _ _ _ _ _ _ _ _.
Answer: (2, -2) or (,)
Tip: The distance from point A to the two coordinate axes is equal, that is, |y|=|x|, which can be converted into y=-x or y=x, and then there are -x=-2x+2 or x=-2x+2, x=2 or x=.
Second, multiple choice questions
7. In the function y=, the value range of the independent variable x is
A.x & gt3 B.x≥3
C.x & gt-3d x ≥- 3
Answer: b
Tip: In order to make radicals meaningful, the number of roots should be greater than or equal to 0.
8. known function y=kx, k
a . y 1 = y2 b . y 1 & lt； y2
c . y 1 & gt； Y2 D. Unable to determine
Answer: b
Hint: k < 0, y decreases with the increase of X.- 1 >-2, then y 1 < y2.
9.(20 10 Jiangsu Suzhou Senior High School Entrance Examination) It is known that the linear function y=kx-k, and if y decreases with the increase of x, the image of this function passes through the _ _ _ _ _ _ _ _ _ _ quadrant.
A. One, two, three B. One, two, four
C. two, three, four D. one, three, four
Answer: b
Hint: y decreases with the increase of x, and then k < 0, showing a downward trend from left to right, and b =-k > 0. The image passes through the positive semi-axis of the Y axis, so a straight line passes through the first, second and fourth quadrants.
10.(20 10) Translate the straight line y=2x upward by two units, and the obtained straight line is
a . y = 2x+2 b . y = 2x-2 c . y = 2(x-2)d . y = 2(x+2)
A: A.
Prompt: The straight line y=2x moves up by two units, that is, the abscissa is unchanged, the ordinate is +2, and y=2x+2.
Third, answer questions.
1 1. The image passing points (1, -4) and (2,5) of the linear function are known.
(1) Find the relationship of linear functions;
(2) Draw the function image.
(1) answer: y = 9x-13;
Tip: It is known to use the undetermined coefficient method to find the relationship between two points. You can set y=kx+b first, when x= 1, y=-4, when x=2, y=5. Substitution is converted into equations k+b=-4, 2k+b=5, and the solution is k=9, b =- 10.
(2)
12. In a certain place, it is found that the relationship between the number of crickets chirping in 1 minute and the local temperature is approximately linear. The following is a comparison table between the number of crickets and the temperature change:
Crickets call for time
…
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 calls 57 times in 1 minute, what is the temperature at that time?
(1) answer: y=7x-2 1.
Tip: With the method of undetermined coefficient, the linear function can be set to y=kx+b, and when y=84, x =15; When y= 1 19, x=20. Substitution is transformed into the equation 15k+b=84, 20k+b= 1 19, and the solution is k=7, b=-2 1.
Answer: The temperature is about 1 1 Celsius.
Tip: When y=57, substitute the function to find x≈ 1 1.
13. Company A has 12 agricultural vehicles and 6 agricultural vehicles in warehouse A and warehouse B respectively, and now it needs to transfer 10 agricultural vehicles to county A and 8 agricultural vehicles to county B. It is known that the freight charges for transferring/kloc-0 agricultural vehicles from warehouse A to counties A and B are 40 yuan and 80 yuan respectively, and they are transferred from warehouse B.
(1) Find the functional relationship between total freight y and x 。
(2) The total freight amount shall not exceed that of 900 yuan. How many transportation schemes are there? Choose the transportation scheme with the lowest total freight. What's the lowest freight?
(1) answer: y=20x+860.
Prompt: If X agricultural vehicles are transferred from warehouse B to county A, then warehouse B will be transferred to county B (6-x), warehouse A will be transferred to county A (10-x) and warehouse A will be transferred to county B (12-( 10-x), that is, x+2 vehicles.
(2) The answer: 20x+860≤900, and the solution is 0≤x≤2. There are three schemes. When x=0, the lowest freight is 860 yuan.
Tip: y here increases with the increase of x, that is, the bigger x, the bigger y, the smaller x, the smaller y, and the lowest freight when x is the smallest.
14. There are two ways to rent books in the book supermarket:
One is to use a membership card (you need to pay by credit card), and the other is to use a book rental card (you don't need to pay by credit card). With these two cards, the relationship between book rental fee Y (yuan) and book rental time X (days) is as shown in the figure (book rental fee = card payment+rent). According to the information provided in Figure 8- 1, answer the following questions:
Figure 8- 1
(1) According to the actual situation, find out the problems existing in the image.
(2) What image does L1and L2 represent respectively?
(3) What is the daily cost of the two ways of borrowing books?
(4) Write the functional relationship between the borrowing cost y (yuan) and the time x (days) with the library card and membership card respectively.
(5) If the service life of both library cards is one year, how to choose these two ways of borrowing books in this year is more cost-effective?
(1) Answer: In practical problems, the image only takes the light L 1 and L2 on the first quadrant and the coordinate axis.
Tip: Pay attention to the difference between mathematical problems and practical problems and the rationality of mathematical explanation of practical problems.
(2) Answer: L 1, L2 refers to using a library card and a membership card respectively.
Tip: There is no need to pay for the book card, and the image passes through the origin.
(3) Answer: 0.5 yuan is charged every day with a library card, and 0.3 yuan is charged every day with a membership card.
Tip: The daily charge for using the library card is 50÷ 100=0.5, and the daily charge for using the membership card is (50-20)÷ 100=0.3.
(4) Answer: L 1: Y = 0.5x, L2: Y = 0.3x+20.
Tip: 0.5 yuan is charged for using the library card every day, and 0.5x； is charged for X days; 0.3 yuan is charged for using the membership card every day, 0.3x for X days, plus 20 yuan card fee.
(5) Answer:/kloc-It is cost-effective to use a library card within 0/00 days, and it is cost-effective to use a membership card outside 0/00 days.
Tip: When y 1=y2, x= 100, that is, the two cards are the same after using 100; /kloc-the image of the book rental card within 0/00 days is below the membership card, indicating that it is cheap to use the book rental card; /kloc-the image of the membership card outside 0/00 days is below the book rental card, which shows that the membership card is cost-effective.