SOLUTION: Find the vertical asymptotes, if any, of the graph of the rational function. f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2 A. {1, -2, -2 + SQRT3, -2 - SQRT5} B. {-1, -2, -2 + SQ

Algebra ->  Rational-functions -> SOLUTION: Find the vertical asymptotes, if any, of the graph of the rational function. f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2 A. {1, -2, -2 + SQRT3, -2 - SQRT5} B. {-1, -2, -2 + SQ      Log On


   

Question 949294: Find the vertical asymptotes, if any, of the graph of the rational function.
f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2
A. {1, -2, -2 + SQRT3, -2 - SQRT5}
B. {-1, -2, -2 + SQRT5, -2 - SQRT5}
C. {-1, 3, -2 +SQRT5 , -2 -SQRT5 }
D. {-1, 2, -2 +SQRT3 , -2 -SQRT3 }
Found 2 solutions by josgarithmetic, Fombitz:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Your f(x) is not a rational function and has no asymptotes. Polynomial functions do not have asymptotes.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think you're looking for the roots and not the asymptotes here, because there are no asymptotes.
graph%28300%2C300%2C-5%2C5%2C-10%2C10%2Cx%5E4+%2B+3x%5E3+-+5x%5E2+-+9x+-+2+%29
Looks like x=-1 and x=2 are both roots.
That greatly narrows the choices of answers down.
I would suggest plugging in each value into the equation to verify that they are indeed solutions.
Example:
x=-1
y=%28-1%29%5E4%2B3%28-1%29%5E3-5%28-1%29%5E2-9%28-1%29-2=1-3-5%2B9-2=0