Answer
Vertical asymptote:$\quad x=0$
Domain :$\quad (0,+\infty)$
Range :$\quad (-\infty,+\infty)$
.
Work Step by Step
(See table 4.5,
Transformations involving Logarithmic Functions)
$f(x)=\log x$
$h(x)=\log x-2=f(x)-2$ so
the graph of $h(x)$ (blue) is obtained
from the graph of f(x) (red)
by
shifting it down by $2$ units.
Vertical asymptote:$\quad x=0$
Domain :$\quad (0,+\infty)$
Range :$\quad (-\infty,+\infty)$