Problem

Exponential and Logarithmic Functions Translating the graph of an exponential function Below is the graph of $y=2^{x}$. Translate it to become the graph of $y=2^{x-3}-1$.

Solution

Step 1 :The function \(y=2^{x-3}-1\) is a transformation of the function \(y=2^{x}\).

Step 2 :The '-3' inside the exponent shifts the graph 3 units to the right.

Step 3 :The '-1' outside the exponent shifts the graph 1 unit down.

Step 4 :\(\boxed{\text{The graph of } y=2^{x-3}-1 \text{ is the graph of } y=2^{x} \text{ shifted 3 units to the right and 1 unit down.}}\)

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Source: https://solvelyapp.com/problems/3tOET7S3xp/

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