Let $f(x)=e^{x}$ Which of the Following Describe How the Function $g(x)=4 e^{6(x-3)}$

Multiple Choice

Let $f(x) =e^{x}$ . Which of the following describe how the function $g(x) =4 e^{6(x-3) }$ transforms the graph of $f$ ?

A) The graph of $f$ is compressed horizontally by a factor of $\frac{1}{6}$ , then shifted to the right 3 units and stretched vertically by a factor of 4 .
B) The graph of $f$ is shifted to the right 3 units, then compressed horizontally by a factor of $\frac{1}{6}$ and stretched vertically by a factor of 4 .
C) The graph of $f$ is compressed vertically by a factor of $4 e^{-18}$ , and compressed horizontally by a factor of $\frac{1}{6}$ .
D) The graph of $f$ is stretched vertically by a factor of 4 , and compressed horizontally by a factor of $\frac{1}{6}$ .