Final answer:
The horizontal asymptote of an exponential function can be identified by examining the behavior of the function as the input values approach positive or negative infinity.
Step-by-step explanation:
The horizontal asymptote of an exponential function can be identified by examining the behavior of the function as the input values (x) approach positive or negative infinity.
If the exponential function has a positive base greater than 1, then the horizontal asymptote is y = 0. For example, the function y = 2^x has a horizontal asymptote at y = 0.
If the exponential function has a base between 0 and 1, then the horizontal asymptote is y = 0 as x approaches positive infinity. For example, the function y = (1/2)^x has a horizontal asymptote at y = 0.
If the exponential function has a base between 0 and 1, then the horizontal asymptote is y = positive infinity as x approaches negative infinity. For example, the function y = (1/2)^x has a horizontal asymptote at y = positive infinity.
It is important to note that if the base of the exponential function is negative, then it does not have a horizontal asymptote.