Mathematical analysis investigates crossings of horizontal asymptotes in rational functions, suggesting predictable behavior of these graphs.
The graph of a rational function in which the degree of the polynomial in the numerator and the degree of the polynomial in the denominator are equal has a horizontal asymptote. We consider whether such a graph will cross a horizontal asymptote, where it crosses the asymptote, and the number of times it crosses the asymptote.
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Indika et al. (2026) studied this question.
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