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

Question

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

Quizplus · Accepted Answer

The domain of the function $f(x) = \frac{2x^2}{x+3}$ is all real numbers except where the denominator is zero, which occurs at $x = -3$. This also means there is a vertical asymptote at $x = -3$. As $x$ approaches infinity, the highest degree terms in the numerator and denominator dominate, leading to a behavior similar to $y = \frac{2x^2}{x} = 2x$, which means the function grows without bound and does not have a horizontal asymptote.

Find the Domain of the Function and Identify Any Vertical f(x)=2x2x+3f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }f(x)=x+32x2​

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