Find the domain of the function and identify any vertical and horizontal asymptotes. $$f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$$
A)The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = 0.
B)The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = $\frac { 1 } { 2 }$ .
C)The domain is all real numbers x.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.
D)The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.
E)The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -2,and no horizontal asymptote.

Question

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$$ ​
A)The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = 0.
B)The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = $\frac { 1 } { 2 }$ .
C)The domain is all real numbers x.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.
D)The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.
E)The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -2,and no horizontal asymptote.

Quizplus · Accepted Answer

The domain excludes values that make the denominator zero, which are x = ±2. The function simplifies to $f(x) = \frac{1}{x+2}$, leading to a vertical asymptote at x = -2. As x approaches infinity, the function approaches 0, indicating a horizontal asymptote at y = 0.

Find the Domain of the Function and Identify Any Vertical f(x)=x−2x2−4f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }f(x)=x2−4x−2​

Find the Domain of the Function and Identify Any Vertical $f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$