Behavior of Rational Functions: Zeros, Poles, and Asymptotes

① This GeoGebra example dynamically illustrates the behavior of rational functions (e.g., f(x)=a(x-b)/(x-c)), focusing on how the graph changes near zeros, vertical asymptotes, and horizontal asymptotes. ② Core mathematical concepts include rational functions, zeros (where numerator equals zero), poles (where denominator equals zero causing vertical asymptotes), horizontal asymptotes (as x tends to infinity), and discontinuities in the graph. ③ Construction details: Based on the summary, LaTeX commands are used for mathematical expressions, with objects b, a, c, f, text1, g, text2, h, and eq1 defined. Functions f and g likely represent the rational expressions, text1 and text2 are labels, and eq1 is an equation object. Parameters a, b, c can be adjusted via sliders to dynamically change coefficients and observe graph transformations. ④ Suitable for high school or pre-calculus students learning function properties, limits, and asymptotes, as well as for teachers to demonstrate rational function behavior in class.