Limits and Continuity: Pre-Calculus Interactive Demo

① This GeoGebra example demonstrates the concepts of limits and continuity through dynamic function graphs and marked points, allowing students to visually explore how a function behaves near a specific x-value and whether it is continuous there. ② Core mathematical concepts include the definition of a limit, continuity conditions, types of discontinuities (removable, jump, infinite), and the behavior of functions as x approaches a target, with additional connections to linear regression, sine functions, and differential equations as pre-calculus topics. ③ Construction details: The example uses the Function command to define functions f, h, and g, the Point command to create key points A, B, C, D, and E, and the Intersect command to compute intersection points between functions or with axes, which are then used to annotate limit values or continuity status on the graph. ④ This resource is ideal for high school pre-calculus or introductory calculus courses, serving as a classroom demonstration or an interactive self-study tool to help students transition from visual intuition to rigorous definitions of limits and continuity.