What are the asymptotes for #f(x) = 3 + log(x+2)#?

1 Answer
Jun 23, 2015

Answer:

For one, the argument of a log-function must be positive.

Explanation:

This means #x> -2# and #x=2# is the corresponding (vertical) asymptote, because you can get as near to 2 as you want.
In "the language" we say:

#lim_(x->2+) f(x)= -oo#

There is no horizontal asymptote, as the log function will grow with #x# getting larger, even though the growth is slow, or:

#lim_(x-> oo) f(x) = + oo#
graph{3+log(x+2) [-5.67, 14.33, -3.32, 6.68]}