Exploring Rational Linear Functions: Effects of Parameters a, b, c, d on f(x)=(a

This GeoGebra example dynamically demonstrates how changing parameters a, b, c, and d affects the graph of the rational linear function f(x)=(ax+b)/(cx+d). The core mathematical concepts include the properties of fractional linear functions (also known as Möbius transformations or hyperbolic functions), such as vertical asymptotes (where the denominator equals zero), horizontal asymptotes (determined by the ratio of leading coefficients), and transformations like translation, scaling, and reflection. The construction uses sliders to control parameters a, b, c, d, and employs the Polygon command to create auxiliary polygons (e.g., asymptote guides or reference rectangles). Text objects (tekst1, tekst2) display current parameter values. Multiple objects (f, e, g, h, i, j, k, l, m, n, p) are used to mark asymptotes, intersection points, or special features. This resource is ideal for high school mathematics lessons on function transformations and rational functions, as well as introductory calculus for pre-university students, providing an intuitive visual understanding of how parameter changes alter the graph's shape and position.