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

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:

Factor out x:

Express 81 as 9^2:

Express the difference between the two squares:

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

Solve for x:

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

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

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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