Question

graph the equation shown below by transforming the given graph of the parent function.
$y = \frac{1}{8} \cdot 2^{x}$

Explanation:

Step1: Rewrite the function

We know that \(\frac{1}{8}=2^{-3}\), so \(y = \frac{1}{8}\cdot2^{x}=2^{x - 3}\).

Step2: Analyze the transformation

For the parent function \(y = 2^{x}\), the transformation \(y=2^{x - h}\) is a horizontal shift. When \(h>0\), it is a shift to the right. Here \(h = 3\), so the graph of \(y = 2^{x}\) is shifted 3 units to the right.

Answer:

Shift the graph of the parent function \(y = 2^{x}\) 3 units to the right.