Describe verbally the transformations that can be used to obtain the graph of $g$ from the graph of $f$.
\[
g(x)=\frac{1}{3} e^{-(x+7)} ; f(x)=e^{-x}
\]
Answer
Final Answer: The graph of \(g(x)\) can be obtained from the graph of \(f(x)\) by a horizontal shift to the left by 7 units and a vertical compression by a factor of 1/3.
Step 1 ：The function g(x) can be obtained from the function f(x) by applying two transformations.
Step 2 ：First, the graph of f(x) is horizontally shifted to the left by 7 units. This is represented by the '+7' inside the exponent in g(x).
Step 3 ：Second, the graph of f(x) is vertically compressed by a factor of 1/3. This is represented by the '1/3' multiplier outside the exponent in g(x).
Step 4 ：Final Answer: The graph of \(g(x)\) can be obtained from the graph of \(f(x)\) by a horizontal shift to the left by 7 units and a vertical compression by a factor of 1/3.
