y=g(x+2) is the graph of y=g(x) translated 2 units left, NOT y=g(-x+2)=g(2-x). In order to obtain g(2-x): Graph g(-x), which you were correct about this, and then translatethisgraph 2 unitsright, so it becomes y=g[-(x-2)]=g(2-x).

That's the theory behind it, but the shortcut to graphing f(a-x) when given f(x), the trick is just to reflect the graph about the line x=a/2 (that's the result of all the translations).

So what you did wrong was graph y=g(2-x) wrong, you need to translate g(-x) two units right, not left (or simply reflect y=g(x) about x=1). Following that simply draw that bit of the graph for x<1.

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