Graph natural log of x

Problem

y=ln(x)

Solution

1. Identify the domain, which for the natural logarithm function is all positive real numbers, x>0

2. Determine the x-intercept by setting y=0 which occurs at ln(1)=0 giving the point (1,0)

3. Identify the vertical asymptote, which occurs as x approaches 0 from the right, where y approaches −∞

4. Plot key points to determine the shape of the curve, such as (e,1) since ln(e)=1 and (1/e,−1) since ln(e(−1))=−1

5. Sketch the curve starting near the vertical asymptote x=0 passing through (1,0) and increasing slowly as x increases.

Final Answer

y=ln(x)

The graph is a curve defined for x>0 that passes through (1,0) and (e,1) with a vertical asymptote at x=0

Want more problems? Check here!