Mathematics

Problem

Let

k

be the function defined by

k(x)=|x-2|

for all real

x

. a. (i) Express

k(x)

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

y=k(x)

for

-2 \le x \le 6

. c. (iii) Find all real numbers

x

for which

k(x)=3

. d. (iv) Determine the range of

k