Final answer:
San Antonio added the most people between 2015 and 2016. Houston is rapidly growing with major corporate headquarters, and the Dallas-Fort Worth-Arlington metro area is the fastest-growing in the Southwest.
Step-by-step explanation:
The Texas city that added the most people between 2015 and 2016 is Houston. Houston is the fourth largest city in the United States and the largest in Texas. It currently has a population of over 2.2 million people and is experiencing rapid growth.
Between 2015 and 2016, several Texas cities added a significant number of people due to the Sun Belt migrations for tertiary-sector jobs and the region's warm climate. Among the options provided, San Antonio was the city that added the most people during this time frame.
While Houston is indeed a rapidly growing city, noted for being the fourth largest in the United States and the largest in Texas with a diverse population and many Fortune 500 companies, the fastest-growing metro area in the Southwest at that time was the Dallas-Fort Worth-Arlington area, according to the US Census Bureau report released on March 22, 2018.