Respuesta :

MrGumby

Answer:

The correct answer is x = 2 and y = 9

Step-by-step explanation:

This is because we cannot put 2 in for x due to the fact that it would make us divide by 0.

Also, we know that y can never equal 9 since the first part of the equation (3/(x - 2)) will always have some value and will never equal 0. Therefore the whole thing will never equal 9.

Using the concepts of vertical and horizontal asymptotes, it is found that the asymptotes of the given graph are x = 2 and y = 9.

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{3}{x - 2} + 9[/tex].

The vertical asymptote is given by:

x - 2 = 0 -> x = 2.

The horizontal asymptote is given by:

[tex]y = \lim_{x \rightarrow \infty} \frac{3}{x - 2} + 9 = \frac{3}{\infty} + 9 = 0 + 9 = 9[/tex]

More can be learned about asymptotes at https://brainly.com/question/16948935

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