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What is the equation of the slant asymptote of the rational function?

f(x)=8x^3−6x^2+6x−5/ 2x^2−1

y=x−3/2

y=4x−3/2

y=x−3

y=4x−3

 

i think its y=4x-3

 Sep 12, 2019
 #1
avatar+104723 
+2

(8x^3−6x^2+6x−5) /  (2x^2−1 )

 

Divide the polynomials....disregard any remainder

 

                      4x   - 3

2x^2  - 1    [   8x^3 -  6x^2  + 6x  - 5  ]

                      8x^3               -4x

                    __________________________

                               -6x^2           -5

                               -6x^2          + 3

                            __________________

                                              10x  - 8

 

The slant asymptote  is   y =  4x - 3

 

This graph confirms this :    https://www.desmos.com/calculator/5xmjxmfwsh

 

 

cool cool cool

 Sep 12, 2019

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