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An asymptote is a line that a curve approaches but never touches. Imagine a graph where a curve gets closer and closer to a straight line as it moves further away from the origin. This straight line is the asymptote. There are three main types of asymptotes: horizontal, vertical, and oblique.

Horizontal asymptotes occur when a function's output approaches a constant value as the input grows infinitely large or small. For example, in the function y = 1/x, the line y = 0 is a horizontal asymptote because as x approaches positive or negative infinity, y approaches 0.

Vertical asymptotes happen when a function's output becomes infinitely large or small as the input approaches a specific value. For instance, in the same function y = 1/x, the line x = 0 is a vertical asymptote because as x approaches 0 from either side, y goes to positive or negative infinity.

Oblique asymptotes, also known as slant asymptotes, occur when a function's graph approaches a straight line that is neither horizontal nor vertical. This typically happens with rational functions where the degree of the numerator is exactly one greater than the degree of the denominator. Asymptotes are crucial tools for understanding the behavior and sketching the graph of functions.