Let $f(x)$ be any function. The graphs of $y = f(x-1)$ and $y = f(-x+1)$ are symmetric about the line:
Step-by-Step Solution
Key Concept: Two graphs y = f(u) and y = f(v) are symmetric about the vertical line x = a if and only if u + v = 2a at corresponding points. Here, (x-1) + (-x+1) = 0 = 2(0), but we must account for the transformation: the axis of symmetry is x = a where a is the midpoint of the x-values producing equal arguments.
Since $-(x-1) = -x+1$, the graphs of $f(x)$ and $f(-(x-1))$ are symmetric about the line $x-1=0$ or $x=1$.
Correct Answer: 3