what is the equation of the asymptote for this function?\nf(x) = ln x + 5\n\na. x = 0\nb. x = -5\nc. y =…

Explanation:

Step1: Recall domain of natural - log function

The domain of $y = \ln x$ is $x>0$. As $x$ approaches $0$ from the right - hand side, $\ln x\to-\infty$.

Step2: Analyze the given function

The function $f(x)=\ln x + 5$ is a vertical shift of $y = \ln x$ by 5 units up. The vertical asymptote is determined by the domain restriction of the natural - log part. Since the domain of $\ln x$ still restricts $x$ from approaching 0 from the left, the vertical asymptote of $y=\ln x + 5$ is $x = 0$.

Answer:

A. $x = 0$