# How do you find the asymptotes for y=3/(2x-1)?

Nov 23, 2016

The vertical asymptote is $x = \frac{1}{2}$
The horizontal asymptote is $y = 0$
No slant asymptote

#### Explanation:

The domain of $y$ is ${D}_{y} = \mathbb{R} - \left\{\frac{1}{2}\right\}$

As you cannot divide by $0$, $x \ne \frac{1}{2}$

So, $x = \frac{1}{2}$ is a vertical asymptote.

The degree of the numerator is $<$ the degree of the denominator, so there is no slant asymptote.

${\lim}_{x \to - \infty} y = {\lim}_{x \to - \infty} \frac{3}{2 x} = {0}^{-}$

${\lim}_{x \to + \infty} y = {\lim}_{x \to + \infty} \frac{3}{2 x} = {0}^{+}$

So $y = 0$ is a horizontal asymptote.

graph{(y-3/(2x-1))(y)=0 [-10, 10, -5, 5]}