Question

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

Answer 1

Graph `f(x)=lnx` with a positive 2 vertical shift.

Explanation:

Graph `f(x)=2+lnx`

First think about the graph of `f(x)=e^x`. It is an increasing exponential with a horizontal asymptote at `y=0` and passes through the point `(color(red)0,color(blue)1)`.
graph{e^x [-10, 10, -5, 5]}

The graph of `f(x)=lnx` is the inverse of `f(x)=e^x` and has a vertical asymptote at `x=0` and passes through the point `(color(blue)1,color(red)0)`
graph{lnx [-10, 10, -5, 5]}

The graph of `f(x)=color(red)2+lnx` is just the vertical transformation of `lnx` shifted up by `color(red)2`. It will also have a vertical asymptote at `x=0` but will pass through the point `(color(blue)1, color(red)(0+2))` or `(color(blue)1, color(red)2)`
graph{lnx+2 [-10, 10, -5, 5]}