+0  
 
0
84
1
avatar

For which value of x does the function \(f(x) = \frac{2x-6}{x^3 - 7x^2 - 2x + 6}\) cross its horizontal asymptote? 

 Mar 5, 2020
 #1
avatar+111436 
+1

We  have  a  "low/ high"  situation....so.....this graph has a horizontal asymptote at  y  = 0

 

So....we need to solve this

 

  2x - 6

______________  =   0

x^3 -7x^2 -2x + 6

 

 

Only  an x value  in the numerator can make this =   0

 

So

 

2x  - 6   = 0       add 6 to both sides

 

2x  = 6  divide both sides  by  2

 

x =   3

 

So....it crosses its horizontal asymptote  at  (3, 0)

 

See the graph here :

 

https://www.desmos.com/calculator/fotxpapass

 

 

 

cool cool cool

 Mar 5, 2020

13 Online Users

avatar