SOLUTION: state the transforamtion necessary to transform f(x)=1/2(2^3x)-4 to g(x)=8^x

 to 

The graph of  is the red graph below



Write that as:



Then as



Then we form h(x) by adding 4 to the right side
which shifts the graph 4 units up




The graph of h(x) is the green graph below



Finally we form g(x) by multiplying the right side of h(x) by 2.



  
which stretches the green graph by a factor of 2.  That's the same as 
if the graph of h(x) were on a rubber sheet and then we stretched the 
rubber sheet to double its size.

So the final graph of  is the blue graph
below:



So the transformation is first to h(x), by adding 4 to the right side:

h(x) = f(x)+4

then the second transformation is from h(x) to g(x), by multiplying the
right side of h(x) by 2, or

g(x) = 2h(x)

then you can substitute f(x)+4 for h(x) and get

g(x) = 2[f(x)+4]

or 

g(x) = 2f(x)+8

Edwin