what is the equation of the horizontal asymptote?

Question

f(x) = (3x⁴+12x³+3x²+4x+9)/(1x⁴+4x³+4x²-2x+6)

what is the equation of the horizontal asympotote y=? 

does the graph f(x) intersect its horizontal asymptote?(yes or no)

at what x values does f(x) intersect its horizontal asymptote? give your answers in increasing order 

Answer 1

The horizontal asymptote can be found by taking the limit:

y = lim{x-->oo} (3x⁴+12x³+3x²+4x+9)/(1x⁴+4x³+4x²-2x+6) = 3

Answer: y = 3 is the equation of horizontal asymptote.

 

There is no intersection between the asymptote and f(x).