Example 3 (1989 National High School League Question) For any function $y=f(x)$, in the same Cartesian coordinate system, the graphs of the functions $y=f(x-1)$ and $y=f(-x+1)$ are always ( ).
A. Symmetric with respect to the $x$-axis
B. Symmetric with respect to the line $x=1$
C. Symmetric with respect to the line $x=-1$
D. Symmetric with respect to the $y$-axis
Solution: Choose B. Reason: Since the graphs of $f(t)$ and $f(-t)$ are symmetric about the line $t=0$, it follows that the graphs of $f(x-1)$ and $f(-x+1)=f[-(x-1)]$ are symmetric about the line $x-1=0$, i.e., $x=1$.