Domain and Range Practice (Part 2): Roots, Log, and Trig/Surface Constraints

This GeoGebra example demonstrates how to determine a function’s domain and range from its formula by identifying the restrictions that make the expression valid, and then relating those restrictions to the visible part of the graph/surface. Key concepts include domain and range, input constraints for root and logarithm functions (e.g., radicand ≥ 0 and logarithm argument > 0), and how output limits are reflected in the plotted behavior. The construction is typically carried out by defining the relevant function(s) or surface in GeoGebra and using graphing/visualization to observe where the graph exists and where it is missing due to invalid inputs; these observed boundaries guide the inferred domain and range. Even though no specific command list is provided in the “construction summary,” the workflow centers on creating function/surface objects and interpreting graph coverage and edge behavior to justify domain/range results. Suitable for late secondary school through early high school learners and for practice/self-study on domain-and-range and function constraint reasoning.