No, that means it's a function (that is, it's not multi-valued), as you are hinting at at the end of your post. The function is even if you can fold the function along the y axis, and the LHS will line up with the RHS. The function is odd if you can rotate the entire function graph 180 degrees, and it will leave the graph unchanged.So, for example, if you take your pencil and slide the pencil across the graph keeping the pencil (or line) vertical at all times and you never touch more than one point on the graph with that pencil, then the graph is even and *may* have y-axis symmetry?

Incidentally, the horizontal line test (the same pencil-thing you mentioned) will tell you if the function is one-to-one.