Answer
$\left.\begin{array}{lll}
& f(x)=\log_{2^{X}} & g(x)=\log_{2}(x-1)+1\\
domain & (0,\infty) & (1,\infty)\\
range & (-\infty,\infty) & (-\infty,\infty)\\
asymptote & x=0 & x=1
\end{array}\right.$
Work Step by Step
1.Create a table for graphing f(x),
plot several points and join with a smooth curve.
2. $g(x)=f(x-1)+1$
The graph g(x) is obtained from f(x) by
(i) shifting it right by 1 unit, then
(ii) shifting up by 1 unit
3. Read the graph for :
$\left.\begin{array}{lll}
& f(x)=\log_{2^{X}} & g(x)=\log_{2}(x-1)+1\\
domain & (0,\infty) & (1,\infty)\\
range & (-\infty,\infty) & (-\infty,\infty)\\
asymptote & x=0 & x=1
\end{array}\right.$
