Question

Pls answer thank you

Answer 1

Option A : $x=-7$ is the equation of the vertical asymptote

Option D : $y=-8$ is the equation of the horizontal asymptote

Explanation:

The given function is $f(x)=\frac{5}{x+7}-8$

The vertical asymptote of the function can be determined by equating the numerator to zero.

Thus, we have,

$x+7=0$

     $x=-7$

Thus, the vertical asymptote of the function is $x=-7$

Hence, Option A is the correct answer.

Now, we shall determine the horizontal asymptote of the function.

If $\lim\ {x \rightarrow \infty}$, then the function $f(x)=\frac{5}{x+7}-8$ becomes,

$\lim _{x \rightarrow \infty} f(x)=\lim _{x \rightarrow \infty} \frac{5}{x+7}-8=-8$

Thus, the horizontal asymptote of the function is $y=-8$

Hence, Option D is the correct answer.