Mathematics

Problem

Let

h:\mathbb{R}\to\mathbb{R}

be given by

h(x)=2+\sin|x|

. a. (i) Sketch the graph of

h

for

-2\pi\le x\le 2\pi

. b. (ii) From your sketch, state the domain of

h

. c. (iii) From your sketch, state the range of

h

. d. (iv) Explain why the range stated in (iii) remains the same for the entire real line.