Domain

Roots of g 1 ( u )

Roots of g 2 ( v )

Accessible region

A

1

0

v 1 < 0 < v 2

× [ v 1 , v 2 ]

2

u 1 < u 2 < 0 < u 3 < u 4

v 1 < 0 < v 2

[ u 1 , u 2 ] [ u 3 , u 4 ] × [ v 1 , v 2 ]

2T

3

u 1 < u 2 < 0 < u 3 < u 4

v 1 < 0 < v 2

[ u 1 , u 2 ] [ u 3 , u 4 ] × [ v 1 , v 2 ]

2T

4

u 1 < 0 < u 2

v 1 < 0 < v 2

[ u 1 , u 2 ] × [ v 1 , v 2 ]

T

5

u 1 < 0 < u 2

v 1 < 0 < v 2

[ u 1 , u 2 ] × [ v 1 , v 2 ]

T

6

u 1 < 0 < u 2

v 1 < 0 < v 2

[ u 1 , u 2 ] × [ v 1 , v 2 ]

T

7

u 1 < 0 < u 2

v 1 < 0 < v 2

[ u 1 , u 2 ] × [ v 1 , v 2 ]

T

8

u 1 < 0 < u 2

v 1 < v 2 < 0 < v 3 < v 4

[ u 1 , u 2 ] × [ v 1 , v 2 ] [ v 3 , v 4 ]

2T

9

u 1 < 0 < u 2

v 1 < v 2 < 0 < v 3 < v 4

[ u 1 , u 2 ] × [ v 1 , v 2 ] [ v 3 , v 4 ]

2T

10

u 1 < 0 < u 2

0

[ u 1 , u 2 ] ×