Ms. Murphy studied at the Pratt Institute, receiving her B.F.A. in 1967. She attended Skowhegan School of Painting and Sculpture during the summer of 1966. Her work is represented in many public collections, including the Whitney Museum of American Art, the Museum of Modern Art, the Metropolitan Museum of Art, the Hirshhorn Museum, and the Phillips Collection. She was awarded National Endowment for the Arts grants in 1979 and 1989, an Ingram Merrill Foundation Grant in 1986, a Guggenheim Fellowship in 1982, and in 2002 was inducted a member of the American Academy of Arts and Letters. Ms. Murphy was appointed senior critic in painting/printmaking at Yale in 1989.