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Hebei province senior high school entrance examination 20 13 mathematics
Solution: (1) Let the analytical expression of the inverse proportional function be y=

k

x

(k>0),

∫A(m, -2) is on y=2x,

∴-2=2m,

∴m=- 1,

∴A(- 1,-2),

Point a is at y=

k

x

Go ahead,

∴k=-2,

The analytical formula of inverse proportional function is y=

2

x

(2) Observing the image, we can know that when the value of the direct proportional function is greater than that of the inverse proportional function, the value range of the independent variable X is-1 < x < 0 or x >1;

(3) The quadrilateral OABC is a diamond.

Proof: ∫A(- 1, -2),

∴OA=

12+22

=

five

From the meaning of the question: CB∨OA and CB=

five

∴CB=OA,

∴ quadrilateral OABC is a parallelogram,

∫C(2, n )= in y =

2

x

Go ahead,

∴n= 1,

∴C(2, 1),

OC=

22+ 12

=

five

∴OC=OA,

A quadrilateral is a diamond.