# How do you graph  y = ln((2x-1)/(x+1))?

Jan 22, 2017

. x-intercept ( y = 0 ) : 1. Vertical asymptotes : $x = \frac{1}{2} \downarrow \mathmr{and} x = - 1 \uparrow$. Horizontal asymptote : $\leftarrow y = \ln 2 \rightarrow$:

#### Explanation:

As $x \to \pm \infty , y = \ln \left(\frac{2 - \frac{1}{x}}{1 + \frac{1}{x}}\right) \to \ln 2$.

As $x \to {\left(\frac{1}{2}\right)}_{+} , y \to - \infty \mathmr{and}$ as

$x \to - {1}_{-} , y \to \infty$

See the asymptotes-inclusive Socratic graph.

graph{(ln((2x-1)/(x+1))-y)(y-ln 2)(x+1+.01y)(x-1/2+.011y)=0 [-5, 5, -2.5, 2.5]}