Answer
Vertical asymptote:$\quad x=-1$
Domain :$\quad (-1,+\infty)$
Range :$\quad (-\infty,+\infty)$
.
Work Step by Step
(See table 4.5,
Transformations involving Logarithmic Functions)
$f(x)=\ln x$
$g(x)=\ln(x+1)=f(x+1)$ so
the graph of $g(x)$ (blue) is obtained
from the graph of f(x) (red)
by
shifting it to the left by $1$ unit.
Vertical asymptote:$\quad x=-1$
Domain :$\quad (-1,+\infty)$
Range :$\quad (-\infty,+\infty)$