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