Answer:
f(x) = -|x -2| +1
Explanation:
The transformation ...
g(x) = f(x -h) +k
translates the function f(x) so that the point on its graph (0, f(0)) is moved to the location (h, k) on the graph of g(x).
The vertex of the "upside down" absolute value function f(x) = -|x| is (0, 0). In your graph, that point has been moved to (h, k) = (2, 1). So, the transformed function is ...
f(x) = -|x -2| +1 . . . . matches the last choice