Western Governors University (WGU) MATH1200 C957 Applied Algebra Practice Exam

A logistic function typically has one horizontal asymptote, which characterizes its behavior as the input value approaches positive or negative infinity; the function approaches a constant value instead of continuing to rise or fall indefinitely.

In the context of the logistic function, which often models population growth, the horizontal asymptote represents a limiting value that the output cannot exceed, which corresponds to the carrying capacity of the environment.

Because the correct choice states that there are two asymptotes, we need to clarify that while the logistic function has one horizontal asymptote (often at the maximum value it can reach), it does not have a vertical asymptote in the traditional sense associated with rational functions or certain other kinds of functions. The logistic function is defined for all real numbers, meaning it does not approach a vertical line; it simply starts from a value and converges towards the horizontal asymptote without any undefined points.

Therefore, the correct understanding is that the logistic function has one horizontal asymptote, guiding its growth as it approaches its maximum limit.

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