Williams 's songs include hits for Three Dog Night ( `` An Old Fashioned Love Song '' , `` Family of Man '' , `` Out in the Country '' ) , Helen Reddy ( `` You and Me Against the World '' ) , and the Carpenters ( `` Rainy Days and Mondays , '' `` I Wo n't Last a Day Without You , '' and `` We 've Only Just Begun '' ) . He wrote many songs with Kenneth Ascher , including `` The Rainbow Connection '' , featured in The Muppet Movie . He is perhaps best known for popular songs performed by a number of groups in the 70 's including Three Dog Night 's `` Just An Old-Fashioned Love Song '' , Helen Reddy 's `` You And Me Against The World '' , and The Carpenters ' `` We 've Only Just Begun '' as well as his contributions to films such as `` Evergreen '' from A Star Is Born and `` Rainbow Connection '' from The Muppet Movie .