Visualizing Positive and Negative Regions of a Function

This example visually demonstrates the regions where a function takes positive and negative values across its domain. The core mathematical concepts include sign analysis of functions, zeros and intersection points, combinations of polynomial and trigonometric expressions, and the areas bounded by the function graph and the coordinate axes. The construction uses GeoGebra commands such as Polynomial to generate random polynomials, Random and Intersect to compute x-intercepts, and If conditions combined with Line and Textfield objects to color-code or annotate the positive and negative regions. Sliders or text fields allow dynamic parameter adjustment, updating the graph in real time. This resource is suitable for upper secondary or pre-university students to understand function sign changes, solution sets of inequalities, and the connection between graphical and algebraic representations, and can be used for classroom demonstrations or independent exploration.