A function satisfies the following conditions: • • • has a vertical asymptote at…

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

Problem

A function rr satisfies the following conditions: • lim⁡x→∞r(x)=3\displaystyle\lim_{x\to\infty}r(x)=3 • lim⁡x→−∞r(x)=−1\displaystyle\lim_{x\to-\infty}r(x)=-1 • rr has a vertical asymptote at x=1x=1 Which of the following formulas could define rr? (a) 4πarctan⁡x+1+1x+1\displaystyle \frac{4}{\pi}\arctan x+1+\frac{1}{x+1} (b) 4πarctan⁡x+1\displaystyle \frac{4}{\pi}\arctan x+1 (c) 4πarctan⁡x+1+1x−1\displaystyle \frac{4}{\pi}\arctan x+1+\frac{1}{x-1} (d) x+2x−1+2\displaystyle \frac{x+2}{x-1}+2

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