In the given graph, the function f(x) is reflected across the x axis.
When there is a reflection across the x axis, the y coordinates will become opposite.
The graph for f(x) is first reflected cross the x axis, and then, shifted to the left.
If a function h(x) is shifted k units to the left, then the translated function is h'(x)=h(x+k).
Since f(x) is reflected across the x axis and shifted to the left by 2 units, the new graph represented by function g(x) is,
[tex]g(x)=-f(x+2)[/tex]
Hence, option D is correct.
