What is asymptote definition?

An asymptote is a straight line or curve that a graph approaches but never touches. In other words, as the graph gets closer and closer to the asymptote, it gets infinitely close but never quite reaches it. Asymptotes can appear in various types of graphs, including linear, quadratic, and exponential functions.

There are three types of asymptotes: vertical, horizontal, and oblique. A vertical asymptote occurs when the function approaches a specific point on the x-axis, but the output becomes infinitely large and does not touch that point. A horizontal asymptote, on the other hand, occurs when the function approaches a specific value as x gets larger or smaller, but never quite reaches that value. Finally, an oblique asymptote occurs when the graph approaches a straight line at an angle, but does not cross it.

Asymptotes can also help us understand the behavior of a function as it approaches infinity or negative infinity. For example, a function with a horizontal asymptote at y=5 will approach 5 as x gets very large or very small. Similarly, a function with a vertical asymptote at x=3 will become more and more steep as x approaches 3, but will never cross that point.