Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.