First, multiple-choice questions:
1, among the following functions, () belongs to the proportional function.
a、y= B、y= C、y= D、y=
2. In the functions y=, y=, y=, y=x+8, the linear function has ().
a， 1 b，2 c，3 d，4
3. If the function y=(m+ 1) +2 is a linear function, the value of m is ().
a、m= 1 B、m=- 1 C、m= 1 D、m≦- 1
4. Given that the straight lines y=2x and y=kx+3 are parallel to each other, the value of k is ().
A, k=-2 B, k=2 C, k = 2 d, and the value of k cannot be determined.
5. The linear function y=kx+b, if k+b= 1, its image must pass through the point ().
a 、(- 1，- 1) B 、( 1， 1) C 、( 1，- 1) D 、( 1， 1)
6, the following groups of functions, and the y axis intersection is the same ().
A, y=5x and y=2x+3 B, y=-2x+4 and y=-2x-4.
C, y= +3 and y=-2x+3 D, y=4x- 1 and y=x+ 1.
7. It is known that the function y=( +2)x, and y increases with x ().
A, increase B, decrease C, D is related to M, uncertainty
8. If the image of linear function y=( 1-2m)x+3 passes through a (,) and b (,), if
a、m0 C、m< D、m >
9. In the known straight line y=, if AB > 0 and AC < 0, then this straight line does not pass through ().
A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant
10, straight line y=-2x+b and the area of the triangle surrounded by two coordinate axes is 4, then the value of b is ().
a、4 B、-4 C、4 D、2
Second, fill in the blanks:
1 and the image of the linear function y=2x+6 intersect with the y axis, and the coordinate of the intersection point is _.
2. Given the image passing through (-1, 1) and (2,3) of the linear function y=kx+b, the relationship of this linear function is _.
3. Translate the straight line y=3x- 1 upward by 3 units to get the straight line _.
4. The image of a linear function passes through the point p (1, 3), and y increases with the increase of x, so write a functional relationship that meets the conditions.
5. Given that point A (1, a) is on the straight line y=-2x+3, then a = _.
6. It is known that point P is y= on a straight line and the distance from point P to Y axis is equal to 3 unit lengths, then the coordinate of point P is _.
7. The image position of the linear function y=kx+b is roughly as shown in the following figure (1), so the value range of k is _, and that of b is _.
(Figure 1) (Figure 2)
8、(2006? Shaoxing) As shown in Figure (2), if the image of linear function y=x+5 passes through P(a, b) and Q(c, d), the value of a(c-d)-b(c-d) is _.
9、(2006? Hangzhou) It is known that y is a linear function of x, and the following table lists some corresponding values, so m = _.
x- 1 0 1
y 1m- 1
10, point A(2, a) is on the image of linear function y=-x+3, and the intersection of the image of linear function and y axis is b, then the area of △AOB is _.
Third, answer questions:
1, the intersection of straight line =kx+b and y axis is the same as the intersection of straight line =2x+3 and y axis, and the intersection of straight line and x axis is symmetrical about the origin. Find the relationship of straight lines.
2. It is known that y =+ is proportional to x+2, which is twice as much as x+ 1. When x=0, y=4. Try to find the relationship between functions y and X. ..
3. It is known that the straight line y=-x+4 intersects with the straight line y=2x-2 at point A, the straight line y=-x+4 intersects with the Y axis at point B, and the straight line y=2x-2 intersects with the X axis at point C. Find the area of the quadrilateral ABOC.
4. It is known that the range of independent variable X of linear function y=kx+b is-1≤x≤5, and the corresponding range of function value is -6≤y≤0. Find out the relationship of this function.
5、(2006? Hengyang) In order to encourage citizens to save water, the water supply company has specially formulated a new water charge standard. The functional relationship between monthly water consumption x (ton) and payable water fee (yuan) is shown in the figure.
(1) Find the functional relationship between Y and X when the monthly water consumption is less than 5 tons;
(2) The monthly water consumption of a resident is 8 tons. How much is the water fee payable?
(Figure 3)
6. The known linear function y=- x+ 12.
(1) Find the length of the line segment between the two intersections of the image and the coordinate axis;
(2) Find the distance from the origin to the image.
7. A new school bought a batch of desks and chairs. The height of the desk and chair satisfies the linear function relation, when the height of the chair
When it is 50㎝, the height of the table is 80 ㎝; When the height of the chair is 55 cm, the height of the table is 85 cm. According to the requirements, the height of the table is not less than 70㎝ and not higher than 100㎝. After measurement, there is a chair with a height of 45㎝. Does it meet the requirements? Please explain the reason with relevant knowledge.
Attached answer:
I. 1-5 BBC BD, 6- 10 cacbc
2. 1, (0,6), 2,3, y = 3x+2,4, the answer is not unique, 5, 1, 6, (-3,5) or (3,3), 7, k > 0, b < 0.
Three. 1, y =-2x+3,2, y = 4x+6,3,5 (unit area)
4.① When x =- 1 and y =-6; When x = 5 and y = 0.
solve
Once.
② When x =- 1 and y = 0; When x = 5 and y =-6.
solve
∴ The relationship of linear function is y=x-5 or y =-x-1;
5 、( 1)y = x； (2) When it exceeds 5 tons, the relationship is y =1.5x-2.5,8 > 5, when x=8 ∴, y = 1.5x8-2.5 = 9.5 ∴ 9.5 yuan, and the water fee that this resident should pay.
6.( 1) Let the intersection of the linear function with the X axis and the Y axis be A and B (omitted) respectively.
When y=0, from 0=- x+ 12, x=5 and the coordinate of point A is (5,0). Similarly, the coordinates of point B are (0, 12), ∴OA=5, OB= 12.
On AB= = 13 from Pythagorean Theorem
(2) Let the distance from the origin to the image be OC,
∴S△AOB= AB×OC= OA×OB
∴ 13OC=5× 12
∴OC=
7. Let the relationship of linear function be y=kx+b, and get it according to the meaning of the question.
solve
∴ The relationship of linear function is y=x+30.
When x=45, y=45+30=75.
And 70 < 75 < 100, ∴ the chair meets the requirements.