Consider the rational function defined by .

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

Problem

Consider the rational function

g:\mathbb R\setminus\{-2\}\to\mathbb R

defined by

g(x)=\dfrac{1}{x+2}+1

. (i) Identify the equations of all vertical and horizontal asymptotes of the graph of

y=g(x)

. (ii) Find the coordinate of the point at which the graph meets the

y

-axis. (iii) Sketch the graph of

y=g(x)

for

-6\le x\le 4

, marking the asymptotes and the intercept obtained in part (ii). (iv) Using the sketch, state the range of

g

and the interval(s) on which the function is decreasing.