An asymptote is a line that a curve approaches arbitrarily closely as it extends to infinity.
Asymptotes can be horizontal, vertical, or oblique (slanted). A function f(x) has a horizontal asymptote y = L if limx→±∞ f(x) = L. Vertical asymptotes occur where the function approaches ±∞ as x approaches a finite value, typically where the denominator is zero. Asymptotes help describe the end behavior of functions and are important in graphing rational functions, exponential functions, and hyperbolas.
The concept of asymptotes was first studied by Apollonius of Perga (200 BCE) in his work on conic sections. The term "asymptote" comes from Greek "asymptotos" meaning "not falling together." John Wallis and Isaac Newton further developed the concept in the 17th century. Asymptotes became important in the development of calculus and limits.