Questions: For the following function, briefly describe how the graph can be a basic logarithmic function. Then, graph the function and state asymptote of the function. f(x)=4 ln x

For the following function, briefly describe how the graph can be a basic logarithmic function. Then, graph the function and state asymptote of the function.

f(x)=4 ln x

Transcript text: For the following function, briefly describe how the graph can be a basic logarithmic function. Then, graph the function and state asymptote of the function. \[ f(x)=4 \ln x \]

Solution

Solution Steps

Step 1: Identify the Function

The given function is $ f(x) = 4 \ln x $.

Step 2: Describe the Graph

The graph of $ f(x) = 4 \ln x $ is a vertical stretching of the basic logarithmic function $ \ln x $ by a factor of 4.

Step 3: State the Asymptote

The vertical asymptote of the function $ f(x) = 4 \ln x $ is the line $ x = 0 $.

Final Answer

The graph of $ f(x) = 4 \ln x $ is a vertical stretching of the basic logarithmic function by a factor of 4, with a vertical asymptote at $ x = 0 $.

{"axisType": 3, "coordSystem": {"xmin": 0.1, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = 4ln(x)"], "latex_expressions": ["$y = 4\\ln(x)$"]}

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