Question

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

Answer 1

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]}