# What are the asymptote(s) of  f(x) = (3x) / (x+4)?

Nov 11, 2015

$f \left(x\right)$ has horizontal asymptote $y = 3$ and vertical asymptote $x = - 4$

#### Explanation:

When $x = - 4$ the denominator of $f \left(x\right)$ is zero and the numerator is non-zero. So this rational function has a vertical asymptote $x = - 4$.

$\frac{3 x}{x + 4} = \frac{3}{1 + \frac{4}{x}} \to 3$ as $x \to \infty$

So $f \left(x\right)$ has a horizontal asymptote $y = 3$

graph{(3x - xy - 4y)(x+4+y0.001)(y-3-x0.001) = 0 [-25.25, 14.75, -7.2, 12.8]}