SOLUTION: Identify all asymptotes and holes in the graph of the following rational function: f(x) = ((2x^3+6x^2)/(x^2-x-12))

Algebra ->  Rational-functions -> SOLUTION: Identify all asymptotes and holes in the graph of the following rational function: f(x) = ((2x^3+6x^2)/(x^2-x-12))      Log On


   

Question 134844: Identify all asymptotes and holes in the graph of the following rational function:
f(x) = ((2x^3+6x^2)/(x^2-x-12))
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Asymptotes occur when the denominator is zero.
So what values of x make the denominator 0?
%28x%5E2-x-12%29+=+0
%28x-4%29%28x%2B3%29+=+0
x = 4, x =-3
asymptotes are the lines x=4 and x=-3
Holes occur when both the numerator and denominator are 0.
%28%282x%5E3%2B6x%5E2%29%2F%28x%5E2-x-12%29%29
+%282x%5E2%28x%2B3%29%29%2F+%28%28x-4%29%28x%2B3%29%29
So we have a hole at x = -3