What's the difference between these 2 graphs?

[mathman100]

I have my original graph f, and I want to make 2 other graphs out of it (each with their own transformations.)
g(x)=2g(1/2x+1)
so it gets stretched vertically by 2, stretched horizontally by 2, goes left 1 and up 1.
But my problem is with h(x)=2[g((x+1)/2)+1)]
What are the transformations made here? Are they the same as g(x)?

 

[Data]

I assume you mean g(x) = 2f(x/2 + 1) and h(x) = 2[g((x+1)/2) + 1]. I don't know why you think that g is vertically shifted (it isn't), but otherwise your description for it is fine.

You can simplify that expression for h(x) to 2g(x/2 + 1/2) + 2. Then substituting in g(x/2 + 1/2) = 2f((x/2 + 1/2)/2 + 1) = 2f(x/4 + 5/4) you get h(x) = 4f(x/4 + 5/4) + 2. That help?

(I am not sure whether I have interpreted your function definitions correctly, so these are just guesses. Are you sure you typed everything out properly? In your post you defined g(x) = 2g(x/2 + 1) which I assume is a typo.)