Graph 2 natural log of 3x

Problem

y=2*ln(3*x)

Solution

1. Identify the parent function and its transformations. The parent function is y=ln(x)

2. Determine the domain by setting the argument of the natural log to be greater than zero.

3*x>0

x>0

3. Find the vertical asymptote by setting the argument to zero.

3*x=0

x=0

4. Find the x-intercept by setting y=0 and solving for x

0=2*ln(3*x)

0=ln(3*x)

e0=3*x

1=3*x

x=1/3

5. Identify transformations applied to the parent function. The factor of 3 inside the natural log represents a horizontal compression by a factor of 1/3 and the coefficient 2 represents a vertical stretch by a factor of 2

6. Plot key points to determine the shape of the curve.
   For x=1

y=2*ln(3)≈2.197

For x=e/3≈0.906

y=2*ln(e)=2

Final Answer

y=2*ln(3*x)

Want more problems? Check here!