Option A : [tex]$x=-7$[/tex] is the equation of the vertical asymptote
Option D : [tex]y=-8[/tex] is the equation of the horizontal asymptote
Explanation:
The given function is [tex]$f(x)=\frac{5}{x+7}-8$[/tex]
The vertical asymptote of the function can be determined by equating the numerator to zero.
Thus, we have,
[tex]x+7=0[/tex]
[tex]x=-7[/tex]
Thus, the vertical asymptote of the function is [tex]x=-7[/tex]
Hence, Option A is the correct answer.
Now, we shall determine the horizontal asymptote of the function.
If [tex]$\lim\ {x \rightarrow \infty}[/tex], then the function [tex]$f(x)=\frac{5}{x+7}-8$[/tex] becomes,
[tex]$\lim _{x \rightarrow \infty} f(x)=\lim _{x \rightarrow \infty} \frac{5}{x+7}-8=-8[/tex]
Thus, the horizontal asymptote of the function is [tex]y=-8[/tex]
Hence, Option D is the correct answer.
