A function has horizontal asymptote as and horizontal asymptote as

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

h

has horizontal asymptote

y=2

x\to\infty

and horizontal asymptote

y=-1

x\to-\infty

. Which of the following formulas could define

h

? (a)

\displaystyle\frac{2x^{2}-1}{x^{2}+1}

(b)

\displaystyle\frac{3}{2}\arctan x+\frac12

(c)

\displaystyle\frac{3}{\pi}\arctan x+\frac12

(d)

\displaystyle\frac{3}{\pi}\arctan x-\frac12