Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$
A)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 0
B)Domain: all real numbers x except x = 9Vertical asymptote: x = 0Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 3Vertical asymptote: x = 0Horizontal asymptote: y = 9
D)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 9
E)Domain: all real numbers x except x = 3Vertical asymptote: x = 3Horizontal asymptote: y = 0

Question

Find the domain of the function and identify any vertical and horizontal asymptotes. 
$f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$ 
A)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 0
B)Domain: all real numbers x except x = 9Vertical asymptote: x = 0Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 3Vertical asymptote: x = 0Horizontal asymptote: y = 9
D)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 9
E)Domain: all real numbers x except x = 3Vertical asymptote: x = 3Horizontal asymptote: y = 0

Quizplus · Accepted Answer

The function $f(x) = \frac{9}{(x - 3)^3}$ is undefined when the denominator is zero, which occurs at $x = 3$, so the domain is all real numbers except $x = 3$. This also means there is a vertical asymptote at $x = 3$. As $x$ approaches infinity or negative infinity, $f(x)$ approaches 0, indicating a horizontal asymptote at $y = 0$.

Find the Domain of the Function and Identify Any Vertical f(x)=9(x−3)3f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }f(x)=(x−3)39​

Find the Domain of the Function and Identify Any Vertical $f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$