Graph 2 natural log of x

Problem

y=2*ln(x)

Solution

1. Identify the parent function, which is y=ln(x) This function has a vertical asymptote at x=0 and passes through the point (1,0)

2. Determine the transformation, which is a vertical stretch by a factor of 2 This means every yvalue of the parent function is multiplied by 2

3. Find key points to plot. When x=1 y=2*ln(1)=0 When x=e≈2.718 y=2*ln(e)=2 When x=1/e≈0.368 y=2*ln(e(−1))=−2

4. Identify the domain and range. The domain is (0,∞) because the argument of a logarithm must be positive. The range is (−∞,∞)

5. Sketch the curve starting near the vertical asymptote x=0 in the fourth quadrant, passing through (1,0) and (e,2) and continuing to rise slowly as x increases.

Final Answer

y=2*ln(x)

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