An asymptote is a line that a curve approaches as it moves towards infinity, but never touches it. There are three types of asymptotes: horizontal, vertical, and oblique.

• Horizontal asymptotes are horizontal lines that the graph of a function approaches as x tends to +∞ or −∞. They are parallel to the x-axis and are of the form y = k, where k is a constant.

• Vertical asymptotes are vertical lines near which the function grows without bound. They are of the form x = k, where k is a constant, and occur when the denominator of a rational function is zero.

• Oblique asymptotes have a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞. They are also called slant asymptotes and occur when the degree of the numerator is exactly one more than the degree of the denominator in a rational function.

The distance between the curve and the asymptote tends to zero as they head to infinity (or −infinity) . Asymptotes are commonly encountered in the study of calculus and can be computed using limits.