Answer
$f(x)= \log_2x$: The red graph
$g(x)= \log_2(x-1)+1$: The blue graph
Work Step by Step
$x=0$ is the vertical asymptote for the function $f$.
$x=1$ is the vertical asymptote for the function $g$.
The domain of the functions are$$D_f=(0, \infty ), \qquad D_g = (1, \infty ).$$The range of the functions are$$R_f=(- \infty, \infty ), \qquad R_g=(- \infty, \infty ).$$
