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Enter the equations of the asymptotes for the function f(x).



f(x)=−2x+4−6

Vertical asymptote:

Horizontal asymptote:

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Answer:

Vertical Asymptote: -4

Horizontal Asymptote: -6

Step-by-step explanation:

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

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