Consider the function given by

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the function

g:\mathbb R\to\mathbb R

given by

g(x)=|x-1|+2

. (i) Sketch the graph of

y=|x-1|

on the same set of axes as the graph of

y=g(x)

. (ii) Using the sketch or otherwise, determine the range of

g

when the domain is

\mathbb R

. (iii) Find the range of

g

when the domain is restricted to the interval

[1,5]