The answer is B.
f(x) = x-1 will give you a graph of linear function also known as "line"
f(x) = -1 will give you the exact graph like the picture. It's the graph of constant function.
f(x) = 1 will give you a graph of constant function like f(x) = -1. However the graph passes (0,-1) , not (0,1)
f(x) = x+1 will give you a graph of linear function.
Linear Function doesn't give you either vertical or horizontal line except for constant one.