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

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Answer 1 · 2018-02-20T21:36:01

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

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]}