Example 5 Given that the function $y=f(x)$ defined on $\mathbf{R}$ satisfies $f(x)-f(2-$ $x)=0$ for any $x \in \mathbf{R}$, is its graph an axis-symmetric figure? If so, write down the equation of the axis of symmetry.
Given that $f(x)-f(2-x)=0$ holds for any $x \in \mathbf{R}$, we have $f(1+x)=f[2-(1+x)]$, which means $f(1+x)=f(1-x)$. Therefore, the graph of the function $y=f(x)$ is symmetric about the line $x=1$.

Key Points for Solving the Problem: For the function $y=f(x)(x \in D)$, if $f(a+x)=f(a-x)$ holds for any $x$ in the domain, then the graph of this function is symmetric about the line $x=a$; if $\frac{1}{2}[f(a+x)+f(a-x)]=b$ holds for any $x$ in the domain, then the graph of this function is symmetric about the point $(a, b)$.