A certain rational function has the following graphical characteristics: • A hole at

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

Problem

x=1

. • A vertical asymptote at

x=3

. • The point

(0,2)

lies on the graph. Which of the following formulas could define such a function? (a)

\displaystyle \frac{(x-1)(x-6)}{x+3}

(b)

\displaystyle \frac{(x-1)(x-6)}{(x-1)(x-3)}

(c)

\displaystyle \frac{x-6}{x-3}

(d)

\displaystyle \frac{(x-1)(x-6)}{x-3}