Final answer:
Pete Rose was the only member of the Cincinnati Reds' "Big Red Machine" who was born and raised in Cincinnati. The team was highly successful in the 1970s, earning the nickname for their dominance in baseball during that time.
Step-by-step explanation:
The only member of the Cincinnati Reds' "Big Red Machine" of the 1970's to be born and raised in Cincinnati was Pete Rose. He played an integral role in the success of the team during that era, which is remembered as one of the most dominant periods for any team in baseball history. The Big Red Machine was the nickname given to the Cincinnati Reds baseball team that dominated the National League from 1970 to 1979, including back-to-back World Series championships in 1975 and 1976.