Is there a way to find the answer without plugging the answer choices?

You can graph y = x+2 but only when x is 0 or larger. This graph is a straight line through (0,2) and (1,3)

Do the same for y = x-2 but only graph this when x is smaller than 0. This graph goes through (-1,-3) and (-2,-4). 

Check out the attached image

As you can see on the graph, it is impossible to generate y = 1. There's a gap between y = -2 and y = 2

An alternative is to notice that if we plug in y = 1 into y = x+2, then we get x = -1, but the problem is that y = x+2 is only possible when x is 0 or larger. We can't have negative values. A similar issue comes up when you plug y = 1 into y = x-2. We get x = 3 which is not in the proper domain defined above.