The facia board extends around the building just below the roof line.
The wood at the edge of the roof is called the Fascia Board.
I am going to guess that you are talking about the fascia board which is usually a 2x6 board
a gutter?
I've run into this on quite a few older architectural gems with spaced roof boards and cedar shakes as the original roof. The crown molding runs at a 45 degree angle from the fascia to the underside of the leading edge of the first roof board. The first roof board is cantilevered just enough to provide a nailer for the top of the crown molding. The trim serves no purpose other than it's ornamental effect and support for the outer edge of the cantilevered first roof board.
Fascia
Wood, or UPVC.
fascia
A rake board is a part of the roof of a house. The rake board is the diagonal board on the side of the roof's overhang.
You are correct, It is called a FASCIA board. It is typically made out of 1x material so you may not find it if you are looking up FASCIA board on HD website.
The purpose of the fascia board is to provide support for the lower edge of the roof and to protect the underlying structure from water damage. It also serves as a finishing element, enhancing the appearance of the exterior of the building.
Eaves- The roof edge from the fascia to the structure’s outside wall. In general terms, the first three feet across a roof is termed the eave.
One of the pitches will have to "kick" out to the other so your Fascia all lines up.