are a very useful tool for discerning between different types of X-ray populations and galaxy properties (e.g., morphological type, age of stellar population) and investigating the nature of the X-ray sources that populate them (e.g., X-ray binaries -XRBs; see review by ). The XLF of late-type star-forming galaxies is usually described by a straight power-law and is associated with a population of high-mass X-ray binaries (HMXBs) located in regions of star formation (e.g., @2002ApJ...577..726Z; @2004ApJ...602..231C; @2007ApJ...661..135Z). Early-type galaxies are best described by an XLF with a broken power-law and a break at a few times 10$^{38}$ erg s$^{-1}$ (attributed to the Eddington luminosity of neutron star XRBs; e.g., @2000ApJ...544L.101S [@2001ApJ...556..533S]), and are thought to be dominated by a population of low-mass XRBs (LMXBs, e.g., @2004ApJ...611..846K [@2010ApJ...721.1523K]; @2004MNRAS.349..146G). Studies to the XLF of different galaxies can also be used to gain insight into the nature of ULXs.

ULX population studies have revealed that many ULXs are associated with young star-forming regions and star-forming galaxies (e.g., @2004ApJS..154..519S [@2009ApJ...703..159S]). They also tend to be found in low-metallicity regions (e.g., @2009MNRAS.400..677Z; @2010ApJ...714.1217B; @2010MNRAS.408..234M). Such low metallicities are required in order to make more massive BHs (e.g., @2003ApJ...591..288H), which shows that it would be possible 