# How do you graph f(x)=2+ln x?

Oct 2, 2016

Graph $f \left(x\right) = \ln x$ with a positive 2 vertical shift.

#### Explanation:

Graph $f \left(x\right) = 2 + \ln x$

First think about the graph of $f \left(x\right) = {e}^{x}$. It is an increasing exponential with a horizontal asymptote at $y = 0$ and passes through the point $\left(\textcolor{red}{0} , \textcolor{b l u e}{1}\right)$.
graph{e^x [-10, 10, -5, 5]}

The graph of $f \left(x\right) = \ln x$ is the inverse of $f \left(x\right) = {e}^{x}$ and has a vertical asymptote at $x = 0$ and passes through the point $\left(\textcolor{b l u e}{1} , \textcolor{red}{0}\right)$
graph{lnx [-10, 10, -5, 5]}

The graph of $f \left(x\right) = \textcolor{red}{2} + \ln x$ is just the vertical transformation of $\ln x$ shifted up by $\textcolor{red}{2}$. It will also have a vertical asymptote at $x = 0$ but will pass through the point $\left(\textcolor{b l u e}{1} , \textcolor{red}{0 + 2}\right)$ or $\left(\textcolor{b l u e}{1} , \textcolor{red}{2}\right)$
graph{lnx+2 [-10, 10, -5, 5]}