What is the job of a fire extinguisher?

Both Option 1 and Option 2 are correct

The correct answer is option 3. Both Option 1 and Option 2 are correct.

The job of a fire extinguisher is to cut off the supply of air, or to bring down the temperature of the fuel, or both.

Notice that the fuel in most cases cannot be eliminated. If, for instance, a building catches fire, the whole building is the fuel.