Question

graphing natural logarithm functions
identify the graph of $y = \ln x+1$.

Explanation:

Step1: Recall properties of $y = \ln x$.

The function $y=\ln x$ has a vertical - asymptote at $x = 0$, passes through the point $(1,0)$ and is an increasing function for $x>0$.

Step2: Analyze $y=\ln x + 1$.

The transformation $y = f(x)+k$ where $k = 1$ shifts the graph of $y = f(x)$ (in this case $y=\ln x$) up by 1 unit. So the graph of $y=\ln x + 1$ has a vertical - asymptote at $x = 0$, passes through the point $(1,1)$ and is an increasing function for $x>0$.

Answer:

The graph that has a vertical asymptote at $x = 0$, passes through the point $(1,1)$ and is increasing for $x>0$ among the given options. Without specific labels on the options, the key characteristics to look for are the vertical asymptote at $x = 0$ and the point $(1,1)$ on the curve.