\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{\left({x}\right)}}\) can be obtained from the graph of \(\displaystyle{{\log}_{{{2}}}{\left({x}\right)}}\) by translating it along the x-axis by 1 unit in the downward direction

In the graph below:

The blue dotted curve represents the graph for \(\displaystyle{y}={{\log}_{{{2}}}{x}}\)

The black solid curve represents the graph for \(\displaystyle{y}=-{1}+{{\log}_{{{2}}}{x}}\)

In the graph below:

The blue dotted curve represents the graph for \(\displaystyle{y}={{\log}_{{{2}}}{x}}\)

The black solid curve represents the graph for \(\displaystyle{y}=-{1}+{{\log}_{{{2}}}{x}}\)