Alicia's Graph: Visualizing Continuity of a Linear Function

① This example dynamically illustrates the continuity of a linear function over the real numbers, showing that its graph is an unbroken straight line with no gaps or jumps. ② Core mathematical concepts include continuity, linear functions (first-degree functions), and the relationship between points and lines. ③ Construction highlights: using GeoGebra commands Line to draw straight lines, CLine for parallel or perpendicular lines, Point to mark key points (A, B, C, D, E, F), and text1/text2 for labels; objects include lines f, u, v, g and point G, allowing users to drag points and observe how function values change continuously with the independent variable. ④ Suitable for middle school (upper grades) and high school introductory lessons on functions and continuity, as well as a visual precursor to calculus concepts in pre-university courses, or as an extension for random experiments and geometric transformations.