What is a Horizontal Asymptote?

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A horizontal asymptote is a straight line that a curve approaches but never reaches as the input values move toward positive or negative infinity. In mathematical functions, particularly in the study of limits, a horizontal asymptote provides insights into the long-term behavior of the function. When a function approaches a constant value as the input increases or decreases without bound, that constant becomes the horizontal asymptote. Horizontal asymptotes are crucial in understanding the end behavior of functions, aiding in the analysis of trends and establishing limits for functions as they extend towards infinity.