what is the asymptote of the graph of $g(x)=ln x + 5$.\na. vertical at $x = e$\nb. vertical at $x = 0$\nc…

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 $g(x)=\ln x + 5$

The behavior of $g(x)$ as $x$ approaches $0$ from the right is $g(x)=\ln x + 5\to-\infty+5=-\infty$. Since the function approaches infinity (or negative infinity) as $x$ approaches a certain value, we are looking for a vertical asymptote. And as $x\to0^{+}$, $g(x)$ has a vertical asymptote.

Answer:

B. vertical at $x = 0$