Function Investigation: Zeros and Intersections with Coordinate Axes

This GeoGebra example demonstrates how to investigate the zeros of a function and its intersection points with the coordinate axes. The core mathematical concepts include the zeros of a function (x-values where the function equals zero), the coordinates of intersections with the x-axis and y-axis, and the relationship between these points and the function's algebraic expression. The construction uses the Intersect command on the function f and the axes (objects a, b, c, etc.) to generate intersection points N1, N2, and T, along with auxiliary lines (ac, d, e, g) and text labels (text1 to text5) to annotate the results. This example is suitable for high school mathematics teaching or self-study on function properties, helping students visually understand the geometric meaning of zeros and intersections, and master basic GeoGebra operations for function analysis.