Graph the logarithmic function.
$$f(x)=1+{\log }_{1/2}x$$

Step 1 ：The function $f(x)=1+{\log }_{1/2}x$ is the inverse of the function $1/2^x$. This means that the graph of ${\log }_b(x)$ will be a reflection of the graph of $b^x$ over the line $y=x$.

Step 2 ：In this case, the base of the logarithm is $1/2$, which means the graph will be a reflection of the graph of $1/2^x$.

Step 3 ：The function also has a vertical shift of 1 unit up, represented by the '+1' in the function. This means that every point on the graph of ${\log }_{1/2}(x)$ will be moved 1 unit up to form the graph of $1+{\log }_{1/2}(x)$.

Step 4 ：We can generate a range of x-values, calculate the corresponding y-values using the function, and then plot these points to create the graph.

Step 5 ：$\boxed{{\displaystyle \text{The graph of the function }f(x)=1+{\log }_{1/2}x\text{ is a reflection of the graph of }1/2^x\text{ over the line }y=x,\text{ shifted 1 unit up.}}}$