Option 1: Increase. Without an atmosphere, there would be no air to trap heat and regulate temperatures on the Earth`s surface. During the day, without the atmosphere to block and absorb some of the incoming heat from the sun, the surface temperature of the Earth would increase significantly. This would cause extreme heat during the daytime. At night, without the atmosphere to retain and redistribute some of that heat back to the surface, the temperature would drop rapidly, resulting in extreme cold. The absence of an atmosphere would lead to a more pronounced difference between the maximum and minimum temperatures during the day and night, resulting in increased temperature extremes. Therefore, option 1 is correct.

Option 2: Decrease. This option is incorrect because, without an atmosphere, the absence of heat-trapping properties would cause temperature extremes to increase rather than decrease.

Option 3: Stay the same. This option is incorrect because, without an atmosphere, there would be no mechanism to regulate temperature, resulting in increased temperature extremes rather than maintaining the same levels.

Option 4: Fluctuate rapidly. This option is incorrect because although the temperature extremes would indeed increase without an atmosphere, the fluctuations would not necessarily happen rapidly.