Final answer:
The United States faced multiple challenges in governing its empire influenced by figures like Alfred Thayer Mahan and strategies like "Big Stick" and "Dollar Diplomacy". Yellow Journalism and economic imperatives also significantly impacted policy and public opinion surrounding imperialism.
Step-by-step explanation:
The United States faced several challenges while governing its empire during the Age of Empire. One pertinent challenge centered around the conceptual and strategic shifts espoused by figures like Alfred Thayer Mahan, who argued for a strong naval power as the foundation of American imperialism. America grappled with the complexities of managing foreign territories following the Spanish-American War, with issues arising from how to integrate these territories, the role of military and economic power, and the ethical considerations of imperialism.
Yellow Journalism played a significant role in shaping public opinion and policy regarding American expansion. This sensationalist style of reporting often exaggerated facts to promote the idea of American superiority and the need for an overseas empire. It also contributed to the challenges in the dissemination of accurate information and thus impacted foreign policy and public support for imperial actions.
During the late 19th and early 20th centuries, the United States sought to expand its influence through means such as Roosevelt's "Big Stick" Foreign Policy and Taft's "Dollar Diplomacy", reflecting different strategies for imperial governance involving the use of military force and economic control, respectively. The shifts from Era 5 to Era 6 in imperialism and the challenges of economic imperialism in East Asia, including the partitioning of China, influenced American policy and required the U.S. to adapt its strategies for empire management.