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The graph of a function \(f\) is shown in the figure below.

The point \(A(-1; 1)\) is on the graph and \(y=-1\) is a horizontal asymptote.

1. Let \(g(x) = f(x-1) + 2\). On the figure, sketch the graph of \(g\).
2. Write down the equation of the asymptote of \(g\).
3. Let \(A^\prime\) be the point on the graph of \(g\) corresponding to point \(A\). Write down the coordinates of \(A^\prime\).