(1) Find the analytic expression of the inverse proportional function.
OC=a,AC=y=k/x=k/a
S δ AOC = | AC | *| OC |/2 =/k/2 = 2, then k=4.
Analytical formula of inverse proportional function y = 4/x.
(2) If the points (-A, Y 1) and (-2A, Y2) are on the image of the inverse proportional function, try to compare the sizes of Y 1 and Y2.
Y 1=4/-A=-4/A
Y2=4/-2A=-2/A
A>0 has-4/a > -2/A, so there is y1>; Y2
If a
AC is perpendicular to the x axis, and the abscissa of c. A is a, so oc = a.
On the inverse proportional function y =k/x,
So AC=k/a
Because AC×OC× 1/2=4
So k=8
Is BD perpendicular to the x axis?
So BD=4/a, AC = 8/a.
The area of quadrilateral ABDC is: (4/a+8/a)*a/2=6.
So the area of the quadrilateral AODB is 6+4= 10.
Because the area of BOD can be easily found as 4.
So the area of AOB is 6.