Consider the function

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

y = \frac{ax+b}{cx+d}

, where

a, b, c, d

are constants and

c \neq 0

. (1) State the domain of the function. (2) State the equation of the vertical asymptote. (3) Find the axes intercepts. (4) Show that for

c \neq 0

\frac{ax+b}{cx+d} = \frac{a}{c} + \frac{b - \frac{ad}{c}}{cx+d}

. Hence explain why the horizontal asymptote is

y = \frac{a}{c}