An asymptote is a line that a curve approaches but never actually touches. It can be horizontal, vertical, or oblique, depending on the behavior of the function as it moves towards infinity or a specific point. Asymptotes help in understanding the end behavior of functions, particularly in mathematics and graphing. In rational functions, vertical asymptotes occur where the function is undefined, typically at values that make the denominator zero. Horizontal asymptotes indicate the value that the function approaches as the input becomes very large or very small. Understanding asymptotes is essential for analyzing the overall shape and behavior of graphs.