Graph f(x) = log base 2 of x

Problem

ƒ(x)=(log_2)(x)

Solution

1. Identify the domain of the function. Since the argument of a logarithm must be positive, the domain is x>0 This implies a vertical asymptote at x=0

2. Determine key points by choosing values for x that are powers of 2

ƒ(1)=(log_2)(1)=0

ƒ(2)=(log_2)(2)=1

ƒ(4)=(log_2)(4)=2

ƒ(0.5)=(log_2)(2(−1))=−1

3. Analyze the behavior of the graph. As x increases, ƒ(x) increases slowly. As x approaches 0 from the right, ƒ(x) approaches −∞

4. Sketch the curve. Plot the points (0.5,−1) (1,0) (2,1) and (4,2) then draw a smooth curve passing through them, approaching the yaxis as a vertical asymptote.

Final Answer

ƒ(x)=(log_2)(x)

The graph is a logarithmic curve passing through (1,0) and (2,1) with a vertical asymptote at x=0

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