select the correct answer. what is the equation of the asymptote for this function? f(x) = ln x + 5\n\na. x…

select the correct answer. what is the equation of the asymptote for this function? f(x) = ln x + 5\n\na. x = 0\nb. x = -5\nc. y = 0\nd. y = -5

select the correct answer. what is the equation of the asymptote for this function? f(x) = ln x + 5\n\na. x = 0\nb. x = -5\nc. y = 0\nd. y = -5

Answer

Answer:

A. $x = 0$

Explanation:

Step1: Recall domain of natural - log

The domain of $y=\ln x$ is $x>0$.

Step2: Analyze vertical asymptote

As $x$ approaches $0$ from the right ($x\to0^{+}$), $\ln x\to-\infty$. For the function $f(x)=\ln x + 5$, the vertical - shift of $5$ units up does not affect the vertical asymptote. So the vertical asymptote is $x = 0$.