Using it's concepts, it is found that:
- There is a vertical asymptote at x = 4.
- There is a horizontal asymptote at y = -6.
What are the asymptotes of a function f(x)?
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
In this problem, the function is given by:
[tex]f(x) = -\frac{2}{x + 4} - 6[/tex]
Hence:
[tex]x + 4 = 0 \rightarrow x = 4[/tex]
There is a vertical asymptote at x = 4.
As for the horizontal:
[tex]y = \lim_{x \rightarrow 0} -\frac{2}{x + 4} - 6 = -\frac{2}{\infty + 4} - 6 = -0 - 6 = -6[/tex]
There is a horizontal asymptote at y = -6.
More can be learned about asymptotes at https://brainly.com/question/16948935
