Point a is a point on the image of the inverse scale function. If the area of △ ABO is 2, the solution of the inverse scale function is obtained

Point a is a point on the image of the inverse scale function. If the area of △ ABO is 2, the solution of the inverse scale function is obtained

Let a coordinate be (x, y), then AB = LXL, OB = Lyl ∵ s △ ABO = AB * ob / 2 = 2 ∵ AB * ob = 4, that is, LXL * Lyl = lxyl = 4, ∵ xy = 4 or xy = - 4 ∵ the analytic formula of inverse proportion function is y = 4 / X or y = - 4 / X. The above is a detailed process. I hope you can directly apply this conclusion in other problems after understanding: if s △ ABO = K / 2, then

Inverse scale function image
If the area of the rectangle is 4, one edge is x and the other is y, which quadrant is the function image of X and y?
The answers are not the same!

First quadrant
x. Y must be greater than zero
Only in the first quadrant

How to prove the symmetry of an inverse scale function image with respect to a straight line

This is a good proof. You should know that a function and its inverse function are symmetric with respect to y = X. as long as you prove that the inverse function of y = 1 / (k * x) is itself, you can prove that the inverse proportion function is symmetric with respect to y = X

The following functions: ① 3x + y = 0, ② y = x + 1 / 3 (third x + 1), ③ y = (K & # 178; + 1) x (k is a constant) is a positive proportional function, why
The following functions: ① 3x + y = 0, ② y = x + 1 / 3 (third x + 1), ③ y = (K & # 178; + 1) x (k is a constant) is a positive proportional function, why

① 、③
Can be reduced to the form of y = KX + B