What happens to an exponential function as x approaches negative infinity?

As x approaches negative infinity in an exponential function of the form ( f(x) = a^x ) where ( a ) is a positive constant greater than 1, the value of the function decreases towards zero. This behavior occurs because as x takes on increasingly negative values, the exponentiation results in smaller and smaller positive numbers.

For example, if ( a = 2 ) and x becomes -1, -2, -3, etc., the values of ( f(x) ) become ( 0.5, 0.25, 0.125 ), respectively, and continue to decrease, getting closer and closer to zero but never actually reaching it. Thus, the limit of the function as x approaches negative infinity is indeed zero, demonstrating why this choice is the correct answer.

The other choices represent different behaviors and do not correspond to the properties of an exponential function as x decreases indefinitely. Therefore, the accurate portrayal of an exponential function's behavior in such a scenario is that it approaches zero.