Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\ln (x+2)-4$
A) Vertical asymptote: $\mathrm{x}=-2$;
Domain: $(-2, \infty)$, Range: $(-\infty, \infty)$
B) Vertical asymptote: $x=-4$;
Domain: $(-4, \infty)$, Range: $(-\infty, \infty)$
C) Vertical asymptote: $\mathrm{x}=4$;
Domain: $(4, \infty)$, Range: $(-\infty, \infty)$
D) Vertical asymptote: $x=2$;
Domain: $(2, \infty)$, Range: $(-\infty, \infty)$

Question

Quizplus · Accepted Answer

The logarithmic function $\ln(x+2)$ is undefined for $x+2 \leq 0$, which means it is undefined for $x \leq -2$. Thus, the vertical asymptote is at $x = -2$, making the domain $(-2, \infty)$. The range of any logarithmic function is $(-\infty, \infty)$.

Determine the Equation of the Vertical Asymptote for the Graph f(x)=ln⁡(x+2)−4f(x)=\ln (x+2)-4f(x)=ln(x+2)−4

Determine the Equation of the Vertical Asymptote for the Graph $f(x)=\ln (x+2)-4$