Using Function Notation to Describe Rules (Part 1): Continuity and Key Points

This example demonstrates how to use function notation to encode a rule that maps inputs to outputs, and how to visualize that mapping by creating and labeling multiple key objects on the GeoGebra canvas. The mathematical focus includes function notation, continuity (for understanding how output behaves without jumps), and real-number interpretation—linking numeric relationships to geometric representations. From the construction summary, it is built around several objects (A1, B1, A2, A3, A4, A5, A6, A7), indicating a workflow that defines multiple points/labels and uses them as the visible outcomes of applying the same function rule at different input values. The result is suitable for students learning to read and construct function-based rules and for teachers using dynamic geometry tools to strengthen the connection between expressions and graphs. Appropriate for middle and high school instruction and related classroom activities.