Practice: Find a Rational Function with Prescribed Features

This example demonstrates how to construct a rational function equation that matches a set of given features (e.g., intercept/point conditions and limit or asymptotic behavior). Students learn to translate graphical and limit-based constraints into an explicit formula and verify the result on the graph. Key concepts include rational functions, function-graph modeling, and limits (to characterize vertical/horizontal behavior near critical points or at infinity). Construction is driven by GeoGebra commands and objects: Textfield to collect inputs and build symbolic expressions, Random to generate/choose feature sets, Intersect to compute relevant intersection points that encode conditions, Remove to delete temporary construction objects for a clean workflow, and Limit to test the required endpoint/asymptotic behaviors. The setup uses computed equations (e.g., eq1, eq2) and interactive UI elements (e.g., InputBox1, buttons, and displayed text objects) to guide solving and checking. Suitable for advanced high school through early undergraduate calculus/algebra topics and for interactive practice or project-based exploration.