Mathematics

Problem

Define

h:\mathbb R\to\mathbb R

h(x)=|x|+|x-2|

. (i) Express

h(x)

explicitly on each of the intervals

(-\infty,0],\;[0,2],\;(2,\infty)

. (ii) Sketch a rough graph of

y=h(x)

on the real line, clearly indicating key points and the shape in each interval. (iii) Using part (i) or the graph, determine the range of

h

. (iv) Is

h

an onto (surjective) function from

\mathbb R

\mathbb R

? Justify your answer.