SOLUTION: I need to work out the asymptotes of y=(x^2-x-4)/(x+1), now i have researched this and found the answer to be x = -1, y = x-2 but i cannot get my working out to reflect this - any

Algebra ->  Graphs -> SOLUTION: I need to work out the asymptotes of y=(x^2-x-4)/(x+1), now i have researched this and found the answer to be x = -1, y = x-2 but i cannot get my working out to reflect this - any       Log On


   

Question 755848: I need to work out the asymptotes of y=(x^2-x-4)/(x+1), now i have researched this and found the answer to be x = -1, y = x-2 but i cannot get my working out to reflect this - any help would be greatly appreciated. Thanks
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
First examine what happens as x approaches but does not reach the value of -1. x cannot be -1 because the denominator of the function would be zero, and that value is not allowed. The graph has a vertical asymptote at x=-1.

Now perform the polynomial division which represents the function. You produce a remainder.

x+1___|__x______-2
______|________________________
______|x^2______-x______-4
_______x^2______x
___________________
________0_______-2x______-4
________________-2x______-2
_______________________________
_______________________-6_____the remainder.

Therefore the equivalent function is y=x-2-%286%2F%28x%2B1%29%29
NOW, what happens to y as x tends toward infinity and what happens to y as x tends toward negative infinity? The remainder approaches zero, and y approaches x-2.
***
***
***Therefore, the SLANT ASYMPTOTE is y=x-2.

Please be aware, the division shown performed above is normal polynomial division, NOT synthetic division. Easier for me to keep thoughts straight this way sometimes.