Given that the image of a function passes through a point (1,2), and the product of the abscissa of the intersection of the image and the X axis and the ordinate of the intersection of the image and the Y axis is 9, the analytic expression of the function is obtained
Let y = KX + B through (1,2)
2=k+b
b=2-k
y=kx+2-k
Intersection with X axis ((K-2) / K, 0)
Intersection with Y-axis (0,2-k)
(k-2)/k×(2-k)=9
k²+5k+4=0
k=-1,k=-4
y=-x+3
y=-4x+6
RELATED INFORMATIONS
- 1. Given that the image of the first-order function passes through a point (1,2), and the product of the abscissa of the intersection of the image and the x-axis and the ordinate of the y-axis is 9, the first-order function can be obtained
- 2. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ .
- 3. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ .
- 4. It is known that the intersection point of the image with the inverse scale function y = K / X and the linear function y = MX + n is a3,4 And the distance from the intersection of the image of the first-order function and the x-axis to the origin is 5 Finding two analytic expressions Find the coordinates of another point and determine what type of angle AOB is
- 5. As shown in the figure, the image of the first-order function y = KX + 2 and the inverse scale function y = K / X intersects a (4, m)
- 6. If the inverse scale function y = K / X intersects with the image of the first-order function y = KX + 2, then the value range of K is Such as the title
- 7. If there is an intersection point between the image of inverse scale function y = 2 / X and the image of primary function y = kx-4, the value range of K is obtained Hope as soon as possible
- 8. It is known that the ordinate of an intersection of the inverse scale function y = KX and the linear function y = 2x + k is - 4, then the value of K is -___ .
- 9. As shown in the figure, it is known that the two vertices of RT △ OAB are a [6,0], B [0,8], O is the origin, and △ OAB rotates 90 ° clockwise around point A. point O arrives at point o ', and point B arrives at point B' (1) Finding the coordinates of point B 丿 (2) Finding the analytic expression of the function corresponding to the line ab 丿
- 10. As shown in the figure, it is a part of the image of an inverse scale function, and points a (1,10) and B (10,1) are its endpoints. (1) find the analytic expression of the function, and write out the value range of the independent variable x; (2) please give an example of life that can be described by the functional relationship of this problem
- 11. It is known that the intersection point of the image and the Y-axis of the linear function y = (3a-7) x + A-2 of X is above the x-axis
- 12. For the first-order function y = (3a-7) x + A-2 of X, the intersection of the image and Y axis is below x, and Y decreases with the increase of X, then the value range of a is______ .
- 13. It is known that the intersection of the image of y = (3a-7) x + A + 1 and the Y axis is above the X axis It is known that the intersection of the image of the first-order function y = (3a-7) x + A + 1 and the y-axis is above the x-axis, and when X1 is less than x2 The corresponding function value y satisfies that Y1 is greater than Y2, and the value range of a is obtained
- 14. The image of a given function passes through the intersection of the line y = - x + 1 and the X axis And the ordinate of the point of intersection with the Y axis is - 2, so we can find the analytic expression of this first-order function
- 15. The image of the linear function y = x + 3 and the area of the triangle surrounded by the x-axis and y-axis are
- 16. As shown in the figure, the minimum area of △ AOB can be obtained when the image of a function of degree passes through the point P (2,3), the positive half axis and a of the intersection x-axis, and the positive half axis and B of the intersection y-axis
- 17. It is known that the area of the triangle formed by the image of the linear function y = - 2x + B [b > 0] and two coordinate axes is equal to 9. Find the solution set of the value of B - 2x + B ≤ 0
- 18. If the image of positive scale function y = KX passes through the point (- 3,4), find the relation of this function
- 19. Given that the function value y of the positive scale function y = KX increases with the increase of X, the image of the first-order function y = K-X is approximately the same
- 20. Given that point a (x, - 4) and point B (3, y) are symmetric about X axis, then the value of X + y is___ .