The vertical asymptote of f(x) is (A) x = 0, –9.
<h3>What is a function?</h3>- 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:
Set the denominator to 0:
Factor out x:
Express 81 as 9^2:
Express the difference between the two squares:
Split, or
or
.
Solve for x:
or
or
.
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
