Final answer:
The endpoint behavior of a function refers to what happens to the function as the input approaches positive or negative infinity. It can be determined by analyzing the behavior of the function near its horizontal asymptotes. The correct option is D.
Step-by-step explanation:
The endpoint behavior of a function refers to what happens to the function as the input (x) approaches positive or negative infinity. To determine the endpoint behavior, we can analyze the behavior of the function as x becomes extremely large or extremely small.
For example, if a function approaches a specific value as x goes to infinity, we say that the function has a horizontal asymptote. Similarly, if a function approaches a specific value as x goes to negative infinity, we also say that the function has a horizontal asymptote. The behavior of the function near these asymptotes helps us understand the range of the function and the presence of any critical points or relative extrema.
Let's consider the function y = 1/x as an example. As x approaches positive infinity, y approaches zero. This indicates that the function has a horizontal asymptote at y = 0. As x approaches negative infinity, y also approaches zero. This confirms the presence of another horizontal asymptote at y = 0. Therefore, the endpoint behavior of this function involves horizontal asymptotes at y = 0.