g(x) = x²
f(x) = 2g(x -3) + 4
The 2 doubles the height of g without increasing the width, so makes f thinner than g. The x-3 shifts g to the right. The +4 shifts the (doubled) g up four units.
OK, let's go through the answers.
A. f is wider. No the 2 makes f thinner.
B. Narrower, good. Vertex moved right 3 and up 4. Sounds right
Answer: B
Let's check the others.
C. Narrower, ok. Left four units, nope.
D. Wider, nope.