A lovely, bust-length portrait painted by Francesco Francia in 1510 pictures a winsome, long-haired boy of 10 named Federigo Gonzaga. Dressed in a black gown over a white chemise and sporting a jauntily tilted cap and a bejeweled gold necklace, he holds the pommel of a sword and gazes dreamily off to his left. Under blue sky and fair-weather clouds, a pastoral sward extends behind him to a city in the far blue haze.

It is one of the most charming pictures in “The Renaissance Portrait from Donatello to Bellini,” a magisterial, intensely thought-provoking display of about 160 works by the most celebrated masters of 15th-century Italian painting and sculpture at the Metropolitan Museum of Art. It also has a remarkable back story. In the year it was painted, the boy’s father, Francesco Gonzaga, ruler of Mantua, was captured by his Venetian enemies. Pope Julius II brokered his release, which was conditional on the young Federigo being sent to Rome as a hostage to ensure that Francesco would not wreak vengeance on Venice.

In anticipation of her son’s absence, his mother, Isabella d’Este, commissioned his portrait to have as a reminder and a consolation. What a terrible ordeal for Isabella, a reader of the brief museum wall label must think. But further discussion in the exhibition’s excellent catalog reveals that it was not so unhappy. Letters and reports indicate that the precocious Federigo’s Roman sojourn was like a stay at an extremely exclusive boarding school. Returned home after three years, he went on to become Duke of Mantua and lived to the ripe old age of 40, whereupon he died of syphilis.

This curious episode tells a lot about the nature and function of portraiture during the Renaissance. Before the 15th century, no one would have thought to create, for merely domestic consumption, a stand-alone likeness of a person whose importance in the larger scheme of things was of such small significance. Portraits were for kings, popes, saints and other luminaries higher up in the cosmic food chain, and their images were meant for official, more or less public display at sites like churches and tombs.