Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .
A)horizontal: y = 2; vertical: x = -2
B)horizontal: x = 1; vertical: none
C)horizontal: none; vertical: none
D)horizontal: y = 1; vertical: none
E)horizontal: y = -2; vertical: x = 1

Question

Quizplus · Accepted Answer

Horizontal asymptotes are found by comparing the degrees of the polynomials in the numerator and denominator. Since the degrees are the same (2), the horizontal asymptote is y = coefficient of $x^2$ in the numerator / coefficient of $x^2$ in the denominator = 1/1 = 1. There are no vertical asymptotes because the denominator $x^2 + 4$ cannot be zero for any real value of x (it's always positive).

Determine the Equations of Any Horizontal and Vertical Asymptotes Of f