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State the vertical asymptote of the rational function. f(x) = quantity x minus four times quantity x plus nine divided by quantity x squared minus one x = 1, x = -1 None x = 4, x = -9 x = -4, x = 9

Guest Apr 19, 2018
edited by Guest  Apr 19, 2018
 #1
avatar+88898 
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I think we have this  :

 

(x - 4)  ( x + 9)                (x - 4)  ( x + 9)

___________      =        ___________

   x^2  - 1                        (x - 1) ( x + 1)

 

The numerator has no effect upon the vertical  asymptotes

 

We will have a vertical  asymptote when the denominator   = 0

 

Note that when  x  = 1    or  x  = -1......one of the factors in the denominator will =  0.......so  ....these are the vertical asymptotes

 

 

cool cool cool

CPhill  Apr 19, 2018

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