Ok, so
We got the initial function:
f ( x ) = sin ( x )
And we got a function g which make some changes to the function f.
g (x) = -1/2 f ( x + 2 ) - 3
So, we're going to analyze each part.
For example, if we have a function f, f(x) and we do the following:
f ( x + 2 ), we are doing a horizontal shift to the left.
If we multiply the last function by 1/2, we are doing a vertical compression. (1/2<1). And we obtain: (1/2) f ( x + 2 )
If we multiply the function by -1, we do a reflection over x-axis. So, it's a vertical reflection. And we obtain: (-1/2) f ( x + 2 )
And finally, If we change the last function to this new one:
(-1/2) f ( x + 2 ) - 3 , We are doing a vertical shift down.