# How do you find all the asymptotes for  (4x)/(x-3) ?

Vertical asymptote: $x = 3$ & Horizontal asymptote: $y = 4$

#### Explanation:

Given function:

$f \left(x\right) = \frac{4 x}{x - 3}$

Setting $x - 3 = 0 \setminus \implies x = 3$

The given function is undefined at $x = 3$ or $x = 3$ is a point of discontinuity.

Hence, the given curve has a vertical asymptote: $x = 3$

Now, the horizontal asymptote:

$y = \setminus {\lim}_{x \setminus \to \setminus \pm \setminus \infty} f \left(x\right)$

$y = \setminus {\lim}_{x \setminus \to \setminus \pm \setminus \infty} \left(\setminus \frac{4 x}{x - 3}\right)$

$y = 4$