Respuesta :

The vertical asymptote of f(x) is (A) x = 0, –9.

What is a function?

  • A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
  • Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

To find the vertical asymptote of f(x):

The vertical asymptotes of a function are the zeroes of the denominator of a rational function

The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]

Set the denominator to 0:

  • [tex]x^{3} -81x=0[/tex]

Factor out x:

  • [tex]x(x^{2} -81)=0[/tex]

Express 81 as 9^2:

  • [tex]x(x^{2} -9^{2} )=0[/tex]

Express the difference between the two squares:

  • [tex]x(x-9)(x+9)[/tex]

Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].

Solve for x:

  • [tex]x=0\\[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].

Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.

(See attachment for the graph of f(x))

Know more about functions here:

https://brainly.com/question/6561461

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The complete question is given below:

Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).

A) x = 0, –9

B) x = –9

C) x = 0, 9

D) x = 9

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