Question

What is the horizontal asymptote of (3x-2)/(x+6)

Answer 1

$f(x)=\dfrac{3x-2}{x+6}\\\\\lim\limits_{x\to\pm\infty}\dfrac{3x-2}{x+6}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(3-\frac{2}{x}\right)}{x\left(1+\frac{6}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{3-\boxed{\frac{2}{x}}^{\to0}}{1+\boxed{\frac{6}{x}}_{\to0}}=\dfrac{3}{1}=3\\\\Answer:\boxed{y=3}$

Answer 2

The horizontal asymptote is y=3