Graph natural log of a

Problem

y=ln(a)

Solution

1. Identify the function as the natural logarithm, where a is the independent variable (horizontal axis) and y is the dependent variable (vertical axis).

2. Determine the domain, which consists of all positive real numbers a>0 because the logarithm of zero or a negative number is undefined.

3. Find the x-intercept by setting y=0 Since ln(1)=0 the graph passes through the point (1,0)

4. Identify the vertical asymptote at a=0 As a approaches 0 from the right, y approaches −∞

5. Plot key points to determine the shape. For example, when a=e≈2.718 y=1 When a=1/e≈0.368 y=−1

6. Sketch the curve as a smooth, increasing function that passes through (1,0) and (e,1) curving concave down across the entire domain.

Final Answer

y=ln(a)

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