Horizontal Translation of Function Graphs

This example demonstrates the horizontal translation of function graphs along the x-axis, visually showing how the graph shifts left or right when the input variable changes. Core mathematical concepts include function transformations, horizontal shifts, the correspondence between algebraic expressions and their graphs, and coordinate-plane geometry. Construction points: the GeoGebra objects f, h, and g are used, where f defines the original function, h serves as the horizontal translation parameter (typically controlled by a slider), and g represents the translated function, commonly constructed as g(x) = f(x − h). Users can dynamically observe how the graph moves as h varies. Suitable for middle school and high school mathematics instruction, classroom demonstrations, inquiry-based learning, and independent practice, helping students develop an intuitive understanding of graph transformations and the connection between algebra and geometry.