Addition and Multiplication with Variables: Dynamic Algebra and Function Graphs

① This GeoGebra example demonstrates addition and multiplication involving variables, showing how algebraic expressions dynamically generate different function graphs and geometric shapes as parameters change. ② Core math concepts include variable operations, linear and quadratic functions, hyperbolas, tangent functions, matrices, and plane figures, emphasizing the connection between algebra and geometry. ③ Construction highlights: uses the If command to create conditional expressions, defines multiple objects (a, b, c, m, n, p, etc.) as variables or parameters, employs text objects (text1 to text7) to display operations, and uses sliders or input boxes for dynamic adjustment, enabling real-time observation of graph changes. ④ Suitable for middle school to university mathematics teaching, helping students understand the role of variables in algebraic operations, function graph transformations, and integrated multi-concept exploration.