Questions: Sketch the logarithmic function f(x)=log2(x) on the graph below.

Transcript text: Sketch the logarithmic function $f(x)=\log_2(x)$ on the graph below.

Solution

Solution Steps

Step 1: Identify the function

The problem asks to identify the correct graph for the function $ g(x) = \log_{10} (x) $.

Step 2: Understand the properties of the function

The logarithmic function $ g(x) = \log_{10} (x) $ has the following properties:

It passes through the point (1, 0) because $ \log_{10} (1) = 0 $.
It has a vertical asymptote at $ x = 0 $ because the logarithm is undefined for non-positive values.
It increases slowly for $ x > 1 $ and decreases rapidly as $ x $ approaches 0 from the right.

Step 3: Analyze the given graphs

Examine each graph to see which one matches the properties of $ g(x) = \log_{10} (x) $:

Graph A: Passes through (1, 0) and has a vertical asymptote at $ x = 0 $.
Graph B: Does not pass through (1, 0) and does not have a vertical asymptote at $ x = 0 $.
Graph C: Passes through (1, 0) and has a vertical asymptote at $ x = 0 $.

Final Answer

The correct graph is either Graph A or Graph C. Since both graphs meet the criteria, we need to choose one. Given the typical representation of $ \log_{10} (x) $, Graph A is the most likely correct answer.

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