Answer the following questions with reference to the functions and defined on .

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Answer the following questions with reference to the functions

f_1(x)=|x|

and

f_2(x)=|x|+5

defined on

\mathbb R

. (i) Define the term “range” of a real-valued function. (ii) Sketch the graph of

y=f_1(x)

and explain, with suitable reasoning, why the range of

f_1

[0,\infty)

. (iii) Using your result from part (ii) or otherwise, determine the complete range of

f_2