the graph of y = ln x and the corresponding points that lie on the graph of f(x)=2 + ln x. points that lie…

the graph of y = ln x and the corresponding points that lie on the graph of f(x)=2 + ln x. points that lie on the graph of y = ln x (type exact answers in simplified form.) corresponding points that lie on the graph of f(x)=2 + ln x (type ordered pairs. type exact answers in simplified form.) (1/e, - 1) (1,0) (e,1) (1,2) (e,3) use the graphing tool to graph the function.

the graph of y = ln x and the corresponding points that lie on the graph of f(x)=2 + ln x. points that lie on the graph of y = ln x (type exact answers in simplified form.) corresponding points that lie on the graph of f(x)=2 + ln x (type ordered pairs. type exact answers in simplified form.) (1/e, - 1) (1,0) (e,1) (1,2) (e,3) use the graphing tool to graph the function.

Answer

Explanation:

Step1: Recall transformation rule

The graph of $f(x)=2 + \ln x$ is a vertical - shift of the graph of $y = \ln x$ by 2 units up. For a point $(x,y)$ on $y=\ln x$, the corresponding point on $f(x)=2+\ln x$ is $(x,y + 2)$.

Step2: Find corresponding point for $(\frac{1}{e},-1)$

Given the point $(\frac{1}{e},-1)$ on $y = \ln x$. For the function $f(x)=2+\ln x$, when $x=\frac{1}{e}$, $y=2+\ln(\frac{1}{e})$. Since $\ln(\frac{1}{e})=- 1$, then $y=2+( - 1)=1$. So the corresponding point is $(\frac{1}{e},1)$.

Answer:

$(\frac{1}{e},1)$