limit as x approaches infinity of f(x) = 0

limit as x approaches infinity of f(x) = 0 . what does this mean when figuring out the horizontal asymptote?

there are two restrictions that 1. limit as x approaches f(x)=1, and limit as x approaches infinity of f(x) = 0 .


The HA is 1 but I don't get why the second part contributes to answering the question