Graphing Absolute Value Functions via Piecewise Logic (Part 1)

This example demonstrates how an absolute value function forms a characteristic V-shaped graph by treating it as piecewise linear behavior, clarifying the relationship between algebraic conditions and geometric shape. Key concepts include absolute value function graph properties, piecewise definitions, equivalent transformations involving quadratic equations/relations, and logic-based rules that determine the vertex (turning point) and the active branch on each side of it. From the construction summary, objects A1, B1, D1, and E1 are used to assemble the graph: A1 and B1 serve as the base references (such as lines or foundational quantities), while D1 and E1 define the critical points/expressions tied to the absolute value branches. By combining these components under the correct conditional structure, GeoGebra produces the full absolute value curve in one coordinate system. Suitable for middle school through early university learners, it is ideal for teaching absolute value functions, function graphing, and logic-guided geometric modeling.