Rational Functions and their Asymptotes

The purpose of this activity is to illustrate the steps needed to graph a Rational Function without using technology tools, by following these steps the user will be able to graph rational functions quickly. The user can type the numerator and denominator of a function in the input boxes. The original functions will display at the left. Initially, use these function graphs to assist you in finding the following: Degree of n(x): ___, Coefficients: Initial _____ Constant _____ Degree of d(x): ___, Coefficients: Initial _____ Constant _____ y-Intercept: ______, Horizontal Asymptotes: ______________ Slant or other End-behavior Asymptote (EBA): ____________ Roots of n(x) or x-intercepts: _____ Roots of d(x) or locate possible vertical asymptotes: _____ Vertical Asymptotes: _____ Removable discontinuities: _____ Intersections with EBA: ________ Once you have determined 1-4 above, check you answers by clicking on the Find Horizontal Asymptote check box. Determine the solutions (roots) n(x) and d(x), determines the x-intercept(s), the vertical asymptote(s), and any removeable discontinuities. Once you have completed steps 5-9, check you solution by clicking on Dislay Roots, Vertical Asymptotes, Holes, and Intersections for f(x) with the End-behavior Asymptote. With this information you will be able to graph the function, f(x)=n(x)d(x) by plotting the x-intercept(s), y-intercept, vertical asymtotes and EBA, and Holes on your graph paper, you should be able to graph f(x). Usually, you will need to find some additional points not discussed here, this is done by finding f(x) where you replace the x with you x-value. The check boxes 3-7 can illustrate this on the graph for you to check. If you want to see the graphs of numerator or denominator click on n(x) and d(x). on the graph.


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Resource Type
asymptotes  exploration  functions  learn-to-determine-wo-tech  practice  rational-functions 
Target Group (Age)
15 – 18
English (United States)
GeoGebra version
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