Find domain and vertical asymptote of LaTeX:  \displaystyle f(x) = \ln{\left(x - 4 \right)} - 9

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 4 units right and 9 units down. This gives the vertical asymptote as LaTeX:  \displaystyle x = 4 and the domain as LaTeX:  \displaystyle (4, \infty)