Then xy=2,
∴k=2,
∴ The analytical formula of inverse proportional function is: y = 2x.
(2) the point B(m, n) is on the image of y = 2x,
∴ n = 2m, namely mn=2,
∫s△ABC = 12m(2? n)= 12m(2? 2m)=m? 1=2,
∴m=3,
∴n=2m=23
∴B's coordinate is (3,23);
(3) Substitute A (1, 2) and B (3, 23) into y=ax- 1 respectively to obtain:
a 1=3,a2=59
So the range of a is 59 < a < 3.