Let be the function defined by for all real .

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

Problem

Let

k

be the function defined by

k(x)=|x-2|

for all real

x

. (i) Express

k(x)

as a piecewise function without the modulus sign. (ii) Sketch the graph of

y=k(x)

for

-2 \le x \le 6

. (iii) Find all real numbers

x

for which

k(x)=3

. (iv) Determine the range of

k