Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$
A)Domain: all real numbers x except x = 0Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
B)Domain: all real numbers x except x = ±7Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = 7
D)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
E)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -49

Question

Find the domain of the function and identify any vertical and horizontal asymptotes. 
 $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$  
A)Domain: all real numbers x except x = 0Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
B)Domain: all real numbers x except x = ±7Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = 7
D)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
E)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -49

Quizplus · Accepted Answer

The domain excludes x = ±7 because the denominator becomes zero at these points, causing the function to be undefined. There are vertical asymptotes at x = ±7 for the same reason. The degree of the numerator is greater than the denominator, so there is no horizontal asymptote.

Find the Domain of the Function and Identify Any Vertical f(x)=x3x2−49f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }f(x)=x2−49x3​

Find the Domain of the Function and Identify Any Vertical $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$