Questions: Draw the graph of the function g(x)=-2(2^x).

Transcript text: Draw the graph of the function $g(x)=-2\left(2^{x}\right)$.

Solution

Solution Steps

Step 1: Identify the function

The given function is $ g(x) = -2 \cdot 2^x $.

Step 2: Analyze the function

The function $ g(x) = -2 \cdot 2^x $ is an exponential function with a negative coefficient. This means the graph will be a reflection of the exponential growth function $ 2^x $ across the x-axis and then scaled by a factor of 2.

Step 3: Determine the correct graph

The graph of $ 2^x $ is an increasing exponential curve.
Reflecting it across the x-axis will make it a decreasing curve.
Scaling by -2 will stretch the curve vertically.

Final Answer

The correct graph is option b.

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