Translation Inside the Modulus: Dynamic Graph Shift

① This GeoGebra example visually demonstrates how the graph of an absolute value function shifts horizontally when a translation is applied inside the modulus, showing the 'left-add, right-subtract' rule. ② The core mathematical concept is function graph transformation, specifically the family y=|x-a| derived from y=|x|, where the V-shaped graph moves right for positive a and left for negative a while preserving its shape. ③ Construction details: using GeoGebra commands, the example defines the base function f, a slider parameter a for the translation amount, the translated function g, an auxiliary object h (possibly for comparison or reference), and a text label text1 to display the expression or explanation. Dragging the slider updates the graph in real time. ④ This is ideal for middle school or high school mathematics lessons on functions and transformations, helping students grasp horizontal shifts, distinguish internal versus external translations, and explore symmetry of absolute value functions.