What about the middle neighborhood:


He's got to hug these walls ( the asymptotes x = -5 and x = 5 )
 


And remember, he's not allowed to cross the x-axis!  So, he CAN'T do any of these things:


possibilities for the middle section of the graph

 

What's left?


graph of f( x ) = ( 2x^2 +5 ) / ( x^2 - 25 )  ...  DONE!


DONE!


YOUR TURN:

 

Graphf( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

(You already have all the pieces!)

Hey, you can check it on the graphing calculator!  Enter it like this:

( x^2 - x - 6 ) / ( x^2 - 1 )