Mathematics

Problem

Let

h(x)=|x-2|+3

. a. (i) Find the vertex of the graph of

y=h(x)

and determine the

x

-intercept(s) and the

y

-intercept. b. (ii) Determine the domain and the range of

h

. c. (iii) Using the information obtained, plot the vertex and intercepts, then sketch the graph of

y=h(x)

for

-2\le x\le 6

, showing clearly the shape and labelling all key points.