Problem

The graph of $y=2^{x}$ is the solid black graph below. Which function represents the dotted graph?

Answer

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Answer

\(\boxed{y = 2^{x+1}}\)

Steps

Step 1 ：Identify the transformation between the solid black graph and the dotted graph

Step 2 ：Notice that the dotted graph is the solid black graph shifted 1 unit to the right and stretched vertically by a factor of 2

Step 3 ：Write the transformation as an equation: \(y = 2(2^{x-1})\)

Step 4 ：Simplify the equation: \(y = 2^{x+1}\)

Step 5 ：\(\boxed{y = 2^{x+1}}\)

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