The three correct answers regarding the possible outcomes for the asteroid as it approaches Jupiter are:
-
The asteroid slows down as it passes around Jupiter.
(Gravitational interactions can lead to a loss of kinetic energy in certain cases.) -
The asteroid enters a stable elliptical orbit around the sun.
(The asteroid may be captured into a new stable orbit around the sun after its encounter with Jupiter.) -
The asteroid continues out of the solar system.
(Depending on the interaction with Jupiter, the asteroid can gain enough velocity to escape the solar system entirely.)
The other options, such as adopting an unusual orbit around the sun, falling into an irregular orbit around Jupiter, or spiraling into the sun, are less likely in the context described.