Graph y = log base 2 of x

Problem

y=(log_2)(x)

Solution

1. Identify the parent function as a logarithmic function with base b=2

2. Determine the domain and range, noting that the argument x must be positive, so the domain is (0,∞) and the range is (−∞,∞)

3. Locate the vertical asymptote, which occurs where the argument is zero, at x=0

4. Calculate key points by choosing values for y and solving for x using the exponential form x=2

5. Substitute y=−1 to get x=2(−1)=0.5 giving the point (0.5,−1)

6. Substitute y=0 to get x=2=1 giving the xintercept at (1,0)

7. Substitute y=1 to get x=2=2 giving the point (2,1)

8. Substitute y=2 to get x=2=4 giving the point (4,2)

9. Plot these points and draw a smooth curve that approaches the y-axis (x=0 as x approaches zero and increases slowly as x increases.

Final Answer

y=(log_2)(x)

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