Answer:
A. to explain the history of the American West
D. to show that explorers from outside the US settled in western North America
E. to examine the contributions of lesser-known explorers
Step-by-step explanation:
From this passage we can infer the author's purpose for writting this book.
First, he wants to explore the time when settlers came, which means he's attempting to explain the history of the region.
Then, he informs the readers about the role conquistadors had, in that way informing us that foreigners also settled in this region. These explorers are less known to the broad audience, so the author attempts to show and explain their contribution as well, beside the role some more famous people had.