WASHINGTON — For decades at the White House, photographs of the president at work and at play have hung throughout the West Wing, and each print soon gives way to a more recent shot. But one picture of President Obama remains after three years.

In the photo, Mr. Obama looks to be bowing to a sharply dressed 5-year-old black boy, who stands erect beside the Oval Office desk, his arm raised to touch the president’s hair — to see if it feels like his. The image has struck so many White House aides and visitors that by popular demand it stays put while others come and go.

As a candidate and as president, Mr. Obama has avoided discussing race except in rare instances when he seemed to have little choice — responding to the racially incendiary words of his former pastor, for example, or to the fatal shooting of an unarmed black teenager in Florida. Some black leaders criticize Mr. Obama for not directly addressing young blacks or proposing policies specifically for them.

Yet the photo is tangible evidence of what polls also show: Mr. Obama remains a potent symbol for blacks, with a deep reservoir of support. As skittish as White House aides often are in discussing race, they also clearly revel in the power of their boss’s example.