A problem of inverse proportion function As shown in the figure, the image of the positive scale function y = 1 / 2 x and the image of the inverse scale function y = K / X (K ≠ 0) in the first quadrant intersect at point a, cross point a to make a vertical line of the X axis, the perpendicular foot is m, and the known area of △ OAM is 1, (1) Finding the analytic expression of inverse proportion function (2) If B is an inverse scale function, and the abscissa of point B is 1 at the point on the first quadrant image (point B does not coincide with point a), find a point P on the X axis to minimize PA + Pb

A problem of inverse proportion function As shown in the figure, the image of the positive scale function y = 1 / 2 x and the image of the inverse scale function y = K / X (K ≠ 0) in the first quadrant intersect at point a, cross point a to make a vertical line of the X axis, the perpendicular foot is m, and the known area of △ OAM is 1, (1) Finding the analytic expression of inverse proportion function (2) If B is an inverse scale function, and the abscissa of point B is 1 at the point on the first quadrant image (point B does not coincide with point a), find a point P on the X axis to minimize PA + Pb

(1) Let a coordinate be (x, y), then △ OAM area = 1 / 2XY = 1, then xy = 2, and inverse scale function y = K / X (K ≠ 0) ∧ k = 2
The analytic expression of inverse proportion function is y = 2 / X
(2) The abscissa of ∵ B is 1, and the ordinate of ∵ B is 2. Because a is the intersection of two functions, the coordinate of a satisfies the analytic expressions of two functions at the same time. The solution is x = ± 2, and a is in the first quadrant, so x = 2, y = 1

How to judge whether it is an inverse proportion function
Y = k × X-1, y = 4 / (3x) y = 3 π / x, where y is not the inverse proportional function of X, which is 1.23 from left to right
Why?

1

How to judge whether it is an inverse proportion function

The opportunity of ordinate and abscissa is about equal to a fixed value
The simple point is x * y = K

How to judge the inverse proportion function?

The definition of inverse proportion function: if the relationship between two variables X and y can be expressed as y = K / X (k is a constant, K ≠ 0), then,
Then y is said to be the inverse proportional function of X