SOLUTION: Find the vertical and cubic asymptotes of the function. y = {{{(x^4 + 7x^3 + 13x^2 + 8x - 6)/(x + 2)}}}

Algebra ->  Rational-functions -> SOLUTION: Find the vertical and cubic asymptotes of the function. y = {{{(x^4 + 7x^3 + 13x^2 + 8x - 6)/(x + 2)}}}      Log On


   



Question 860503: Find the vertical and cubic asymptotes of the function.
y = %28x%5E4+%2B+7x%5E3+%2B+13x%5E2+%2B+8x+-+6%29%2F%28x+%2B+2%29

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Dividing x%5E4+%2B+7x%5E3+%2B+13x%5E2+%2B+8x+-+6 by x%2B2
we get x%5E3+%2B+5x%5E2+%2B+3x+%2B2 with a remainder of -10 .
That means
.
The vertical asymptote is x%2B2=0<-->x=-2 ,
and the function's graph "hugs" the graph of
f%28x%29=x%5E3+%2B+5x%5E2+%2B+3x+%2B2 as abs%28x%29 increases.