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

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Answer 1 · 2016-03-03T12:57:02

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

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]}

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