y = f(2x) - 1

We start with 

y = f(x)

We replace x by 2x, which shrinks the graph horizonally by a factor of 1/2.  That gives us

y = f(2x)

We subtract 1 from the entire right side, which shifts the graph 1 unit vertically downward.  That gives us

y = f(2x) - 1 

Edwin