As shown in the figure, we know that point a (3, n) is on the image of inverse scale function y = 12x. (1) find the coordinates of point a; (2) if the image of a first-order function passing through point a intersects with the positive half axis of Y axis at point B, and ob = OA, find the analytic expression of this first-order function

As shown in the figure, we know that point a (3, n) is on the image of inverse scale function y = 12x. (1) find the coordinates of point a; (2) if the image of a first-order function passing through point a intersects with the positive half axis of Y axis at point B, and ob = OA, find the analytic expression of this first-order function

(1) ∵ point a (3, n) is on the image with inverse scale function y = 12x, and ∵ n = 123 = 4 ∵ the coordinates of point a are (3, 4) ∵ (3 points) (2) according to Pythagorean theorem oa2 = 32 + 42, so OA = 5 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ∵ ob = OA, and the coordinate of point B on the positive half axis of y-axis is (0,5). Suppose the analytic expression of line AB is y = KX + B, then ∵ 3K + B = 4B = 5, and the solution is k = − 13b = 5. The analytic expression of line AB is y = - 13X + 5

The analytic expression of inverse scale function for the image of inverse scale function y = K / X and the image of y = 3 / X about X-axis symmetry

Take a point a (3,1) on y = 3 / x, because y = K / X and y = 3 / X are symmetric about X axis, so the point B (3, - 1) symmetric about X axis with a must be on y = K / X. so k = - 3, that is y = - 3 / X

There are two intersections A and B between the image of positive scale function y = x and the image of inverse scale function y = K / x, and the abscissa of point a is 21. Find the inverse scale function y when x = - 4
Value of

Let a (2, m), because a is on y = x, so m =, 2., that is, a (2,2).. because a is on y = K / x, so k = 4, that is, y = 4 / X. so when x = - 4, the value of inverse proportional function y = 4 / X is - 1

If we know that the inverse proportion function y = k of X, when x = 1 / 3 of negative, y = - 6, we can find: 1) the analytic expression of this function. 2) if it is a linear function
The image with the number y = mx-4 and the image with the inverse scale function y = K / X in (1) have intersection points

1) Substituting x = - 1 / 3, y = - 6 into y = K / x,
The solution is k = 2
So y = 2 / X
2) The equations y = mx-4 and y = 2 / X are combined,
We get MX ^ 2-4x-2 = 0
If two images have intersection, then (- 4) ^ 2-4 * m * (- 2) ≥ 0
The solution is m ≥ - 2
And y = mx-4 is a linear function, m ≠ 0
So the value range of M is m ≥ - 2 and m ≠ 0