Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .
A)horizontal: y = -2; vertical: x = 5
B)horizontal: x = 2 and x = -2; vertical: y = -5
C)horizontal: y = 5; vertical: x = 2 and x = -2
D)horizontal: x = -5; vertical: y = 2 and y = -2
E)horizontal: y = 5; vertical: x = 2

Question

Quizplus · Accepted Answer

Horizontal asymptotes are found by dividing the leading coefficients of the highest degree terms when the degree of the numerator and denominator are the same, which gives $y = \frac{5}{1} = 5$. Vertical asymptotes occur where the denominator equals zero and the numerator is not zero at the same points, which happens at $x^2 - 4 = 0$, or $x = \pm 2$.

Determine the Equations of the Vertical and Horizontal Asymptotes of the Graph