Vertical Asymptote (Defined as a Limit)

This GeoGebra applet demonstrates the formal definition of a vertical asymptote as a special type of nonexistent limit. It shows how a function approaches positive or negative infinity as the input approaches a specific value, making the vertical line an asymptote. The core mathematical concepts are limits, one-sided limits, and asymptotic behavior. The construction uses the Point command to define key points and multiple text objects (text1, text2, etc.) to display limit expressions and function values. Dynamic parameters a and b allow users to manipulate the function and observe how the graph behaves near the asymptote. This resource is ideal for high school or introductory college calculus students to grasp the connection between limits and graphical features, and can be used for classroom demonstrations or self-paced exploration.