Answer
$$
y=\frac{4x}{3-2x}
$$
We find that:
Asymptotic: $y=-2$ and $x=\frac{3}{2}$
$x$-intercept: 0
$y$ -intercept: 0
Work Step by Step
$$
y=\frac{4x}{3-2x}
$$
The function is undefined for $x=\frac{3}{2}$, so the line $x=\frac{3}{2}$ is a vertical asymptotic..
To find a horizontal asymptotic, let $x$ get larger and larger, so that
$$
y=\lim _{x \rightarrow \infty} \frac{4x}{3-2x}=-2
$$
This means that the line $y=-2 $ is a horizontal asymptotic.
When $x=0 $ the $y$-intercept is 0
When $y=0 $ the $x$-intercept is 0
So,
Asymptotic: $y=-2$ and $x=\frac{3}{2}$
$x$-intercept: 0
$y$ -intercept: 0
