Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9

Sagot :

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

#SPJ4

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

View image tutorconsortium33
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.