Let be defined by for .

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

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

f(x)=\dfrac{|x-2|}{x-2}

for

x\neq2

. (i) Simplify

f(x)

separately for

x>2

and for

x<2

. (ii) Name the parent function family represented by the simplified form and justify your answer using two distinct properties. (iii) Determine the domain and range of

f

and draw a rough sketch of its graph on the number line, indicating all key points. (iv) State, with reason, whether

f

is even, odd or neither.

Related theory

Types of Functions
Functions
Special Functions

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