Looking at the two graphs in the image, you are asked to identify the transformation of $f(x)$ to obtain $g(x)$, specifically by finding constants $A$ and $B$ in the equation $g(x) = A f(Bx)$.

Analysis:

1. Vertical transformation (affecting $A$):

   • The graph of $f(x)$ appears to be stretched or compressed vertically to create $g(x)$. Comparing the slopes or distances from the x-axis will give an indication of the vertical scaling factor $A$.

2. Horizontal transformation (affecting $B$):

   • The graph of $f(x)$ might also be horizontally stretched or compressed to form $g(x)$, meaning $B$ controls this horizontal scaling.
   • If there is a reflection (a flip over the y-axis), $B$ could also be negative.

To Find $A$ and $B$:

• Look at specific points on both graphs to compare how the input (x) and output (y) are transformed from $f(x)$ to $g(x)$.
• For example, pick a point like $(1,1)$ or $(2,4)$ on $f(x)$ and see where it maps to on $g(x)$.

Let's break it down step by step:

1. Find a corresponding point on both graphs.
2. Determine how much the function is stretched/compressed or flipped vertically (for $A$).
3. Check how the x-values are scaled or flipped (for $B$).

Would you like me to walk you through the graph comparison to extract specific values for $A$ and $B$?