DETROIT — Coleman A. Young II was settling into a diner booth with a mug of hot chocolate heaped with whipped cream when a stranger approached. “I adored your father, and I hope you’re just like him,” she said. Hours later, as Mr. Young rode in a car along a neighborhood street, someone called out, “I voted for your dad, man!” And when he stood before residents of an apartment complex, a woman rose to recount her memories of Mr. Young’s father, Coleman A. Young, Detroit’s first black mayor. “He made a whole lot of difference in this city,” she said.

Coleman Young II, 34, wants to be the next mayor of Detroit. He has served in the Michigan Legislature for a decade, first as a representative and now as a senator, but his father, who died in 1997 after serving two decades as mayor, still looms over nearly everything about this campaign. A large photo of the elder Mr. Young, with his confident, trademark gaze, holds the prime spot on the wall of the campaign headquarters of his son, who shakes voters’ hands wearing the “Mayor Coleman A. Young” cuff links and the “CY” lapel pin that his father once wore.

Matters of legacy and loyalty would be enough to propel the plot of an entire mayoral race in most places. Rarely, though, has an American city seen as much tumult and change as suddenly as Detroit, which has lurched in only a few years from being the nation’s largest city ever to file for bankruptcy to experiencing a downtown building boom, and from watching its population base vanish to seeing, at least in some parts, home prices rise. Detroit’s mayoral election on Tuesday comes at a pivot point for the city.

The vote will reveal how much change residents see in Detroit, where 40 percent of the streetlights were broken five years ago and the average police response time was nearly an hour. It will speak to race in a city that is 82 percent black, pitting the incumbent, Mike Duggan, who in 2013 was elected Detroit’s first white mayor in 40 years, against Mr. Young and a cast of lesser-known candidates. And the election will be a test of how Detroiters perceive their remade city, a place where a hollowed downtown has been transformed into a tourist draw, complete with a manufactured beach and new streetcars, but where thousands of vacant, decrepit houses still fill neighborhoods across its 139 square miles.