what type of reaction occurs when potassium metal reacts with fluorine gas?

Answer 1

Exothermic synthesis.

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That is Sodium and chlorine, potassium is more reactive than sodium, and fluorine is more reactive than chlorine.

Answer 2

2K + F2 ==> 2KF
This is a synthesis reaction.
See this for a review of different types of reactions.
http://www.usoe.k12.ut.us/CURR/science/sciber00/8th/matter/sciber/chemtype.htm