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Rational-Functions-and-Asymptotes

Page history last edited by Kristen Fouss 11 years, 7 months ago

Rational Functions and Asymptotes

 

Rational function notation is f(x)= N(x)/D(x)!!!!  A rational function is formed when a polynomial is divided by another polynomial. 

                                                                                                         

                                                                                                                                                  

         An asymptote is a line that a graph approaches

                          and HARDLY ever crosses.

 

                      Check out this cool asymptote!

 

 

                   

                   To find a verticle asymptote, set the the denominator=0

                        ( A graph will NEVER cross a vertical asymptote!)

 

                         Ex:                                                       f(x)=    2x^2+11

                                                                                    x^2+x-20

                      vertical asymptotes: x=-5  x=4                                  

                                                                           

                                                                         f(x)=    2x^2+11

                                                                                    (x+5)(x-4)    

 

                                                                                         x+5=0          x-4=0

                                                                       x=-5                 x=4   

 

For more help with graphing and more examples of graphs visit:   http://home.alltel.net/okrebs/page192.html 

 

 

To find a horizontal asymptote, compare the degrees of the numerator and denominator. 

 

                                                           IF...

 

          The numerator is less than the denominator then the horizontal asymptote is y=0               ex.  4x^2+3h.a  y=0

                                                                                                                                                                               3x^3+5

 

          The numerator is greater than the denominator there is no horizontal asymptote         ex. 2x^3+5  h.a  none

                                                                                                                                                                        x^2+x+20

 

          The numerator is equal to the denominator the horizontal asymptote= the coefficient of numerator degree

                                                                                                                                       the coefficient of denominator degree      

                                                                                                                                                                 ex. 2x^2+7             h.a   y= 2

                                                                                                                                      5x^2+3                            5

 

 

                    Finding the Domain is easy!

 

                Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work.

        1. Find vertical asymptotes

        2. Give all possible x's in parenthetic notation and exclude the vertical asymptotes

 

Ex.                                                    f(x)=   2x^2+3           f(x)=  2x^2+3         vertical asymp.  x=-5    x=4

                                                                 x^2+x-20                 (x+5)(x-4)

                                    

                        DOMAIN: (-¥ ,-5)U(-5,4)U(4,¥ )

 

 

 

To learn more about Rational Functions and Asymptotes visit this very informative website: http://people.richland.edu/james/lecture/m116/polynomials/rational.html

 

                                                     Here is a video to help you better understand solving and graphing asymptotes

 

                                            YouTube plugin error                                                            

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