identify the graph of y = ln x + 1

Explanation:

Step1: Recall parent - function properties

The parent function of $y = \ln x+1$ is $y=\ln x$. The domain of $y = \ln x$ is $x>0$, and it passes through the point $(1,0)$ with a vertical asymptote at $x = 0$.

Step2: Analyze vertical shift

The function $y=\ln x + 1$ is a vertical shift of the function $y=\ln x$ up by 1 unit. So, it passes through the point $(1,1)$ (since when $x = 1$, $y=\ln(1)+1=0 + 1=1$) and still has a vertical asymptote at $x = 0$.

Answer:

The graph that passes through the point $(1,1)$ and has a vertical asymptote at $x = 0$ and is an increasing function for $x>0$. Without seeing the specific details of the options, look for a graph that has these characteristics.