Find domain and vertical asymptote of LaTeX:  \displaystyle f(x) = \ln{\left(x + 6 \right)} + 5

The base function LaTeX:  \displaystyle \ln(x) has vertical asymptote LaTeX:  \displaystyle x =0 and domain LaTeX:  \displaystyle (0, \infty) . LaTeX:  \displaystyle f(x) is shifted 6 units left and 5 units up. This gives the vertical asymptote as LaTeX:  \displaystyle x = -6 and the domain as LaTeX:  \displaystyle (-6, \infty)