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

Feb 4, 2017

The vertical asymptote is $x = 1$
The horizontal asymptote is $y = 2$
No slant asymptote

#### Explanation:

As you cannot divide by $0$, $x \ne 1$

The vertical asymptote is $x = 1$

As the degree of the numerator $=$ the degree of the denominator,

there is no slant asymptote.

${\lim}_{x \to \pm \infty} f \left(x\right) = {\lim}_{x \to \pm \infty} \frac{2 x}{x} = 2$

The horizontal asymptote is $y = 2$

graph{(y-(2x+1)/(x-1))(y-2)(y-100x+100)=0 [-18.02, 18.03, -9.01, 9.01]}