"The article says this is a swing district. What are this districts voting patterns?"
The district leans Republican, having given President Bush 53% in 2004. Its rural precincts are far more conservative than its Tucson precincts, but heavily democrat West Tucson is in the Hispanic-majority AZ-07 and thus the Tucson precincts in the AZ-08 are fairly evenly split between Republicans and Democrats. There is no reason why a conservative Republican with strong positions against illegal immigration such as Graf should not defeat a liberal Democrat such as Giffords in the AZ-08.