Graph natural log of y

Problem

x=ln(y)

Solution

1. Identify the relationship between the variables. The task is to graph the natural logarithm of y which is typically expressed as x=ln(y)

2. Rewrite the equation in exponential form to make it easier to plot points. Since the natural log is the inverse of the exponential function with base e the equation is equivalent to y=ex

3. Determine the domain and range. For the natural log function ln(y) the input y must be strictly positive (y>0. The output x can be any real number.

4. Identify key points for the graph. When x=0 y=e0=1 When x=1 y=e1≈2.718 When x=−1 y=e(−1)≈0.368

5. Recognize the asymptote. As x approaches negative infinity, y approaches 0 This means the xaxis (where y=0 is a horizontal asymptote for the function y=ex or a vertical asymptote at y=0 for the relation x=ln(y) relative to the yaxis.

6. Sketch the curve. The graph is a smooth, increasing curve that passes through (0,1) and (1,e) plotted on a coordinate system where the horizontal axis is x and the vertical axis is y

Final Answer

y=ex

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