These are the old gutters. Because of this big gap between the drip edge and the gutters the water was able to run behind the gutters and onto the soffit and possibly into the house. This would have caused rotting and mold if left like this. We removed these gutters and replaced them with new seamless aluminum gutters. We installed the new ones up behind the drip edge. Because there was no fascia board we strapped them to the roof and took extra time to put the straps and screws under the shingles. Putting the straps under the shingles means no holes in the shingles and no unsightly straps on the shingles.
Homeowners often find that after getting a new roof they have problems with the gutters. Roofers often rehang the gutters but do not do it correctly. It is a good idea to get the gutters inspected after a new roof to make sure they are working correctly.