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 = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -2
B)Domain: all real numbers x except x = -3 Vertical asymptote: x = -3
Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: No horizontal asymptote
D)Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 2
E)Domain: all real numbers x Vertical asymptote: x = -3
Horizontal 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 = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -2
B)Domain: all real numbers x except x = -3 Vertical asymptote: x = -3
Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: No horizontal asymptote
D)Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 2
E)Domain: all real numbers x Vertical asymptote: x = -3
Horizontal asymptote: y = 0

Quizplus · Accepted Answer

The domain of the function is all real numbers except where the denominator equals zero, which is at x = -3, leading to a vertical asymptote at x = -3. As $x$ approaches infinity, the highest degree terms in the numerator and denominator are $2x^2$ and $x$, respectively, indicating the function grows without bound and does not approach a constant value, hence no 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 $f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }$