Question

1
select the correct answer
what is the equation of the asymptote for this function?
f(x) = ln x + 5

a. x = 0
b. x = -5
c. y = 0
d. y = -5

Explanation:

Step1: Recall the property of natural - log function

The natural - log function \(y = \ln x\) has a vertical asymptote at \(x = 0\).

Step2: Analyze the transformation of the function

The function \(f(x)=\ln x + 5\) is a vertical shift of the function \(y=\ln x\) up by 5 units. The vertical asymptote of \(y = \ln x\) is not affected by vertical shifts. So the vertical asymptote of \(f(x)=\ln x + 5\) is still \(x = 0\).

Answer:

A. \(x = 0\)