Find the horizontal and vertical asymptotes of the graph.
A) Vertical asymptotes: x = 2 and x = - 2; Horizontal asymptote: y = 3
B) Horizontal asymptotes: y = 2 and y = - 2; Vertical asymptote: x = 1
C) Horizontal asymptotes: y = 2 and y = - 2
D) Vertical asymptotes: x = 2 and x = - 2; Horizontal asymptote: y = 1

Question

Find the horizontal and vertical asymptotes of the graph. 
A) Vertical asymptotes: x = 2 and x = - 2; Horizontal asymptote: y = 3 
B) Horizontal asymptotes: y = 2 and y = - 2; Vertical asymptote: x = 1 
C) Horizontal asymptotes: y = 2 and y = - 2 
D) Vertical asymptotes: x = 2 and x = - 2; Horizontal asymptote: y = 1

Quizplus · Accepted Answer

The graph has vertical asymptotes at x = 2 and x = -2 because those are the values that make the denominator equal to 0. The horizontal asymptote can be found by looking at the highest degree terms in the numerator and denominator. In this case, both the numerator and denominator have degree 2, so we divide the leading coefficients to find the horizontal asymptote: 5/5 = 1. Therefore, the horizontal asymptote is y = 1. Choice D is the only option that matches this criteria.

Find the Horizontal and Vertical Asymptotes of the Graph