Let , where . Which of the following statements accurately summarizes all key…

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

p(x)=\dfrac{x^{2}-4}{x+1}

, where

x\neq -1

. Which of the following statements accurately summarizes *all* key features of the graph of

y=p(x)

? (a) Vertical asymptote at

x=-1

x

-intercepts at

x=\pm2

, horizontal asymptote

y=1

, and no local extrema. (b) Vertical asymptote at

x=-1

x

-intercepts at

x=\pm2

, oblique asymptote

y=x-1

, and no local extrema. (c) Vertical asymptote at

x=-1

, removable discontinuity at

x=2

, oblique asymptote

y=x-1

, and a local minimum at

x=0

. (d) Vertical asymptote at

x=1

x

-intercepts at

x=\pm2

, oblique asymptote

y=x-1

, and no local extrema.