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 $y=2^{x-3}-1$.

Answer

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Answer

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

Steps

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