Final answer:
The Federal Trade Commission (FTC) would investigate a local company for giving false information in their ads, as they are responsible for protecting consumers against deceptive advertising practices.
Step-by-step explanation:
The agency that would investigate claims that a local company is giving false information in one of their ads is the Federal Trade Commission (FTC). The FTC is responsible for checking factual claims about a product's performance to protect consumers from false advertising and deceptive practices. Language and images that are exaggerated or ambiguous, but not outright false, are allowed in advertising. However, completely untrue "facts" are not permitted, and it's the FTC's job to enforce these rules.