The basic function has a f(x+4) term. This
results in a shift of four in the negative direction. The grey graph shows the original function, and the blue graph shows the current function. 

The
0.5 coefficent in front of the f (x+4) causes all the y values to be
scaled down 1/2. Compress the graph vertically by this factor.


The last  1 term indicates that all the y
values should be shifted down one. Translate the graph 1 unit downward. 

This is a comparison of the original graph
and the new translated graph. 