Let be defined by .

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

Problem

Let

f: \mathbb R \to \mathbb R

be defined by

f(x)=|x|

. (i) Identify the standard type of function represented by

f

. (ii) Explain, with one algebraic reason and one graphical reason, why

f

is not classified as a polynomial function of degree

1

even though on each half of the x-axis its graph resembles a straight line. (iii) Determine the domain and range of

f

. (iv) Is

f

one-one? Justify your answer.