$R(x) = \lambda_2$ for all $x$

$\lambda_1 \leq R(x) \leq \lambda_3$ for all nonzero $x$

$R(x)$ depends only on the norm of $x$, not its direction

The minimum of $R(x)$ is $\lambda_1$ and the maximum is $\lambda_3$, achieved only when $x$ is an eigenvector