Questions: Use the function below to answer the following questions. p(x) = 2^(x-3) - 1 (a) Use transformations of the graph of y = 2^x to graph the given function.

Use the function below to answer the following questions.
p(x) = 2^(x-3) - 1
(a) Use transformations of the graph of y = 2^x to graph the given function.
Transcript text: Use the function below to answer the following questions. \[ p(x)=2^{x-3}-1 \] (a) Use transformations of the graph of $y=2^{x}$ to graph the given function.
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Solution

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Solution Steps

Step 1: Identify the Base Function

The base function is y=2x y = 2^x .

Step 2: Apply Horizontal Shift

The function p(x)=2x31 p(x) = 2^{x-3} - 1 involves a horizontal shift. The term x3 x-3 indicates a shift to the right by 3 units.

Step 3: Apply Vertical Shift

The function also involves a vertical shift. The term 1-1 indicates a shift downward by 1 unit.

Final Answer

The function p(x)=2x31 p(x) = 2^{x-3} - 1 is obtained by shifting the graph of y=2x y = 2^x to the right by 3 units and downward by 1 unit.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = 2**(x-3) - 1"], "latex_expressions": ["y=2x31y = 2^{x-3} - 1"]}

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