Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\ln (x-2)+5$
A) Vertical asymptote: $\mathrm{x}=-5$;
Domain: $(-\infty,-5)$, Range: $(-\infty, \infty)$
B) Vertical asymptote: $x=5$;
Domain: $(5, \infty)$, Range: $(-\infty, \infty)$
C) Vertical asymptote: $\mathrm{x}=2$;
Domain: $(-\infty, 2)$, Range: $(-\infty, \infty)$
D) Vertical asymptote: $\mathrm{x}=2$;
Domain: $(2, \infty)$, Range: $(-\infty, \infty)$

Question

Quizplus · Accepted Answer

The logarithmic function $\ln(x-2)+5$ is undefined for $x-2 \leq 0$, meaning it is defined for $x > 2$. Thus, the vertical asymptote is at $x=2$, the domain is $(2, \infty)$, and the range of any logarithmic function is $(-\infty, \infty)$.

Determine the Equation of the Vertical Asymptote for the Graph f(x)=ln⁡(x−2)+5f(x)=\ln (x-2)+5f(x)=ln(x−2)+5

Determine the Equation of the Vertical Asymptote for the Graph $f(x)=\ln (x-2)+5$