SOLUTION: For the function g(x) = x^3/(2x^3-x^2-3x) determine a. the vertical asymptotes, if any b. the holes, if any c. the horizontal asymptotes, if any d. the oblique asymptote, if a

Algebra ->  Average -> SOLUTION: For the function g(x) = x^3/(2x^3-x^2-3x) determine a. the vertical asymptotes, if any b. the holes, if any c. the horizontal asymptotes, if any d. the oblique asymptote, if a      Log On


   

Question 1115363: For the function g(x) = x^3/(2x^3-x^2-3x) determine
a. the vertical asymptotes, if any
b. the holes, if any
c. the horizontal asymptotes, if any
d. the oblique asymptote, if any
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Some factorization will help to identify some of those details.

%28x%2Ax%5E2%29%2F%28x%2A%282x%5E2-x-3%29%29

highlight_green%28%28x%2Fx%29%28%28x%5E2%29%2F%282x-3%29%28x%2B1%29%29%29

Undefined for x at 0, but since there is x%2Fx, a HOLE at x = 0.

Notice degree of numerator and denominator of g(x) are the same, so horizontal asymptote is y=1%2F2.

Vertical asymptotes: Look at the denominator of the factored form.
Asymptotes for x=-1 and for x=3%2F2.