functions with absolute value

hello! I just had 2 homework questions that had to do with absolute value.

the first one was finding the domain and range of f(x)=|x|/x but instead of a getting a piecewise function graph, it got a greatest integer function graph (step graph). I thought all absolute value gave the graph a v shape? also I'm confused how to plug number into this graph if someone could give me and example id appreciate it (:

secondly, I had another question that was f(x)=x+6/|x+6| and it asked for the domain and range. how do I plug numbers into this equation if the bottom is absolute value? if I do the same thing on top and bottom it would give me things like 6/6 or 7/7 which would always equal one.