Question

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

Answer 1

. x-intercept ( y = 0 ) : 1. Vertical asymptotes : `x = 1/2 darr and x = -1uarr`. Horizontal asymptote : `larr y = ln 2 rarr`:

Explanation:

As `x to +-oo, y = ln ((2-1/x)/(1+1/x)) to ln 2`.

As `x to (1/2)_+, y to -oo and` as

`x to -1_-, y to oo`

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]}