Question

The graph of the function f(x)= (x^2+5x+4)/(2x^3-2x^2-12)
has a horizontal asymptote. If the graph crosses this asymptote, give the x-coordinate(s) of the intersection. Otherwise, state that the graph does not cross the asymptote.

Answer 1

horizontal asymptote is y = 0 because the degree of the denominator is bigger than the degree of the numerator

Answer 2

and it does cross it because if you set thing beast = 0 and solve you will get x=-4 or x = -1

Answer 3

that is correct! can you show me how you calc'd pls; got stuck with the x^3

Answer 4

\[\frac{x^2+5x+4}{2x^3-2x^2-12}=\frac{(x+4)(x+1)}{2x^3-12x^2-12}\]\]

Answer 5

the denominator doesn't factor unless you count factoring out the two

Answer 6

i means it doesn't factor over the rationals

Answer 7

the denominator is a cubic polynomial with one real zero. how you find it is a mystery to me. there is a formula, but it is a pain and this denominator does not factor. but we know at least 3 things: the horizontal asymptote is y = 0, and it crosses that line twice at -4 and -1. to find the zero of the denominator graph it.