Question

How do you find the domain, x intercept and vertical asymptotes of `f(x)=lnx+2`?

Answer 1

The `lnx`-function only accepts positive values of `x`

Explanation:

There is no upper limit to `x` so the domain is:
`0 < x < oo`

As `x` gets smaller the value of `lnx` gets more and more negative, or in 'the language':

`lim_(x->0) lnx=-oo`

Meaning `x=0` is the (only) vertical asymptote

The `x-`intercept is when `lnx+2=0->lnx=-2`
This means that `x=e^(-2)~~0.135...`

The range of the function is from `-oo` to `+oo`

graph{ln x+2 [-7.78, 8.026, -3.534, 4.37]}