Example 3 Given the function $f(x)=\left\{\begin{array}{l}2^{x}(x \leqslant 1), \\ \log _{\frac{1}{2}} x(x>1),\end{array}\right.$ then the graph of the function $y=f(1-x)$ is $(\quad)$.
(A)
(B)
(C)
(D)
Solve: Draw the graph of $y=f(x)$. Since $f(1-x)=f(-(x-1))$, we obtain the graph that is symmetric to the graph of $y=f(x)$ with respect to the $y$-axis, and then shift it one unit to the right. Choose D.