  We study both function theoretic and spectral properties on complete
noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with nonnegative
Bakry-\'{E}mery Ricci curvature. Among other things, we derive a gradient
estimate for positive $f$-harmonic functions and obtain as a consequence the
strong Liouville property under the optimal sublinear growth assumption on $f.$
We also establish a sharp upper bound of the bottom spectrum of the
$f$-Laplacian in terms of the linear growth rate of $f.$ Moreover, we show that
if equality holds and $M$ is not connected at infinity, then $M$ must be a
cylinder. As an application, we conclude steady Ricci solitons must be
connected at infinity.
