Let be the function with the restricted domain .

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

Problem

Let

p

be the function

p(x)=\dfrac{6x-9}{2x+3}

with the restricted domain

x>0

. (i) Show that

p

possesses a vertical asymptote and state its equation. (ii) Obtain an explicit expression for

x

in terms of

y

from the equation

p(x)=y

. (iii) Using the condition

x>0

, deduce the range of

p