Approximate the horizontal asymptote of .
A) -8
B) 8
C) -11
D) 2
E) 11

Question

Approximate the horizontal asymptote of  .
A) -8 
B) 8 
C) -11 
D) 2 
E) 11

Quizplus · Accepted Answer

To approximate the horizontal asymptote, we look at the degree of the highest power of the variable in the numerator (which is 1) and the denominator (which is $\sqrt{x^2+1}$). As $x$ becomes very large (positive or negative), the denominator becomes dominated by the $x$ term, and so the function behaves like $\frac{1}{\sqrt{x}}$, which tends towards $0$ as $x$ gets large. Therefore, the horizontal asymptote is at $y=11$.

Approximate the Horizontal Asymptote of