How do you find the asymptotes for #[(3x^2) + 14x + 4] / [x+2]#?

1 Answer
Mar 3, 2016

Answer:

One vertical asymptote #x+2=0# and one slanting asymptote given by #y=3x#.

Explanation:

To find the asymptotes of #(3x^2+14x+4)/(x+2)#

we first observe the denominator #(x+2)#, which shows that the function has one vertical asymptote #x+2=0#.

Further, highest degree of numerator is two and that of denominator is one, and their ratio is #3x^2/x=3x#.

Hence, we have a slanting asymptote given by #y=3x#

graph{(3x^2+14x+4)/(x+2) [-10, 10, -5, 5]}