identify the graph of y = ln x + 1.
identify the graph of y = ln x + 1.
Answer
Explanation:
Step1: Recall properties of $y = \ln x$
The domain of $y=\ln x$ is $x>0$, it passes through the point $(1,0)$ and is an increasing - function.
Step2: Analyze $y=\ln x + 1$
The graph of $y = f(x)+c$ (where $c = 1$ here) is a vertical shift of the graph of $y = f(x)$ upwards by $c$ units. So the graph of $y=\ln x + 1$ has a $y$ - intercept at $(0,1)$ (since when $x = 1$, $y=\ln(1)+1=0 + 1=1$) and is still an increasing function with domain $x>0$.
Answer:
The graph that has a $y$ - intercept at $(0,1)$ and is increasing for $x>0$ (the third graph among the given options if we assume the graphs are numbered from left - to - right).