Problem
Exponential Function Manipulation Quiz (1) (3) (4) (6) (5) Question 3 The function $f$ is given by $f(x)=2^{z}$, and the function $g$ is given by $g(x)=\frac{f(x)}{8}$. For which of the following transformations is the graph of $g$ the image of the graph of (A) A horizontal translation to the left 3 units (B) A horizontal translation to the right 3 units (C) A vertical translation up $\frac{1}{8}$ unit (D) A vertical translation down $\frac{1}{8}$ unit
Solution
Step 1 ：Given the function \(g(x)=\frac{f(x)}{8}=\frac{2^{z}}{8}=2^{z-3}\)
Step 2 ：This is equivalent to the function \(f(x)\), but with the exponent decreased by 3
Step 3 ：In terms of graph transformations, decreasing the exponent of a function corresponds to a horizontal shift to the right
Step 4 ：Therefore, the correct answer is \(\boxed{\text{A horizontal translation to the right 3 units}}\)
