To get a certain function I have to reflect the other one using the x axis and then shift it up 3 values. Represent that analytically

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The following picture shows $h(x)$ and $g(x)$:

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Which of the following is true?

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I think that to get from g to h I have to replect g horizontaly and then shift it up by 3, because the asymptote becomes $y=-1$. So I think the solution is B), but my book states it's A. What did I do wrong?