Answer
Vertical asymptote:$\quad x=-1$
The domain of g:$\quad (-1,+\infty),$
The range of g:$\quad (-\infty,+\infty),$
.
Work Step by Step
(See table 4.5,
Transformations involving Logarithmic functions)
$g(x)=\log_{2}(x+1)=f(x+1)$ so
the graph of g(x) (blue) is obtained
from the graph of f(x) (red)
by
shifting it one unit to the left.
Vertical asymptote:$\quad x=-1$
The domain of g:$\quad (-1,+\infty),$
The range of g:$\quad (-\infty,+\infty),$