# How do you find the Vertical, Horizontal, and Oblique Asymptote given y=(3x+1)/(2-x)?

Feb 3, 2017

The vertical asymptote is $x = 2$
The horizontal asymptote is $y = - 3$
No oblique asymptote

#### Explanation:

As you cannot divide by $0$, $x \ne 2$

The vertical asymptote is $x = 2$

As the degree of the numerator is $=$ to the degree of the denominator, there is nooblique asymptote.

${\lim}_{x \to \pm \infty} y = {\lim}_{x \to \pm \infty} \frac{3 x}{-} x = - 3$

Therefore,

the horizontal asymptote is $y = - 3$

graph{(y-(3x+1)/(2-x))(y+3)(y+50x-100)=0 [-20.62, 19.94, -10.68, 9.6]}