  We obtain an analytical equation of state for one-dimensional strongly
attractive Fermi gas for all parameter regime in current experiments. From the
equation of state we derive universal scaling functions that control whole
thermodynamical properties in quantum critical regimes and illustrate physical
origin of quantum criticality. It turns out that the critical properties of the
system are described by these of free fermions and those of mixtures of
fermions with mass $m$ and $2m$. We also show how these critical properties of
bulk systems can be revealed from the density profile of trapped Fermi gas at
finite temperatures and can be used to determine the T=0 phase boundaries
without any arbitrariness.
