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

Answer:

B. vertical at (x = 0)

Explanation:

Step1: Recall the domain of natural - log function

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

Step2: Analyze the behavior of (g(x)=\ln(x)+5)

As (x\to0^{+}), (\ln(x)\to-\infty). So, (g(x)=\ln(x) + 5\to-\infty) as (x\to0^{+}).

Step3: Determine the asymptote

The graph of (y = g(x)=\ln(x)+5) has a vertical asymptote at (x = 0). There is no horizontal asymptote for (y=\ln(x)+5) since (\lim_{x\to+\infty}\ln(x)+5=+\infty) and (\lim_{x\to0^{+}}\ln(x)+5 = -\infty).