Graph the logarithmic function.
\[
f(x)=4+\log _{1/2} x
\]

Plot two points on the graph of the function

Step 1 ：Understand the properties of the given logarithmic function \(f(x)=4+\log _{1/2} x\). The base of the logarithm is 1/2, which means the function is decreasing. The '+4' outside the logarithm indicates a vertical shift 4 units up.

Step 2 ：Choose some convenient values for x to plot points on the graph. Let's choose x=1 and x=2.

Step 3 ：When x=1, the function is undefined because log base 1/2 of 1 is 0. So, the y-value for x=1 is 4.0. This means that the point (1,4) lies on the graph of the function.

Step 4 ：When x=2, the function is equal to 4 + log base 1/2 of 2. So, the y-value for x=2 is 3.0. This means that the point (2,3) lies on the graph of the function.

Step 5 ：\(\boxed{\text{Final Answer: The points (1,4) and (2,3) are on the graph of the function } f(x)=4+\log _{1/2} x}\)