Questions: Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. f(x) = 2^(x+5) - 2 Describe how the graph of the function can be obtained from the graph of a basic exponential function. Start with the graph of y = 2^x. Shift it left 5 units and then shift it down 2 units. Use the graphing tool to graph the equation.

Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. f(x) = 2^(x+5) - 2 Describe how the graph of the function can be obtained from the graph of a basic exponential function. Start with the graph of y = 2^x. Shift it left 5 units and then shift it down 2 units. Use the graphing tool to graph the equation.
Transcript text: Part 2 of 2 Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of th can be obtained from the graph of a basic exponential function. \[ f(x)=2^{x+5}-2 \] Describe how the graph of the function can be obtained from the graph of a basic exponential function. Start with the graph of $y=2^{x}$. Shift it left 5 units and then shift it down 2 units. Use the graphing tool to graph the equation.
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Solution

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Solution Steps

Step 1: Identify the Basic Exponential Function

The basic exponential function is \( y = 2^x \).

Step 2: Apply Horizontal Shift

Shift the graph of \( y = 2^x \) to the left by 5 units. This results in the function \( y = 2^{(x+5)} \).

Step 3: Apply Vertical Shift

Shift the graph of \( y = 2^{(x+5)} \) down by 2 units. This results in the final function \( y = 2^{(x+5)} - 2 \).

Final Answer

The graph of the function \( f(x) = 2^{x+5} - 2 \) can be obtained by shifting the graph of \( y = 2^x \) left by 5 units and then down by 2 units.

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