Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.
A) y = 0; crosses at (±1, 0)
B) y = 2; crosses at
C) y = 2; does not cross
D) No horizontal asymptote

Question

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses. 
A) y = 0; crosses at (±1, 0) 
B) y = 2; crosses at 
C) y = 2; does not cross 
D) No horizontal asymptote

Quizplus · Accepted Answer

The function has a horizontal asymptote at y=2 because as x gets very large (positive or negative), the denominator grows faster than the numerator, so the fraction approaches 0. Since the numerator is always positive, the graph approaches y=2 but never crosses it. Therefore, option C is the best choice.

Determine the Location of the Horizontal Asymptote If It Exists