Field-Of-View
The FOV doesn't change. The interval between one point in k-space and the next (Δkx, in the x-direction) doesn't change, and FOVx = 1/Δkx.
Δkx = γ.Gx.ΔTs, (units m-1) where γ is the gyromagnetic ratio, Gx is the gradient strength in the x-direction, and ΔTs is the "sampling interval": the time to sample just one point of one line in k-space.
All we lose is spatial resolution.
Further reading on this topic:
Books: MRI From Picture to Proton p128, MRI The Basics p160-165, 251