Find the domain and the vertical asymptote of the function.
-$$g ( x ) = \ln ( x - 8 )$$
A) Domain: $( 8 , \infty )$; vertical asymptote: $x = 8$
B) Domain: $( - \infty , \infty )$; vertical asymptote: none
C) Domain: $( - 8 , \infty )$; vertical asymptote: $x = - 8$
D) Domain: $( 0 , \infty )$; vertical asymptote: $x = 0$

Question

Quizplus · Accepted Answer

The natural logarithm function $\ln(x)$ is defined for $x > 0$. For $\ln(x - 8)$, the argument $x - 8$ must be greater than 0, which means $x > 8$. Therefore, the domain is $(8, \infty)$. The function approaches negative infinity as $x$ approaches 8 from the right, indicating a vertical asymptote at $x = 8$.

Find the Domain and the Vertical Asymptote of the Function g(x)=ln⁡(x−8)g ( x ) = \ln ( x - 8 )g(x)=ln(x−8)

Find the Domain and the Vertical Asymptote of the Function $g ( x ) = \ln ( x - 8 )$