Find domain and vertical asymptote of LaTeX:  \displaystyle f(x) = \ln{\left(x - 8 \right)} - 7

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 8 units right and 7 units down. This gives the vertical asymptote as LaTeX:  \displaystyle x = 8 and the domain as LaTeX:  \displaystyle (8, \infty)