code for diagram

> FF:=piecewise(x<-3,-(x+3)^2+1,x<-1,sin(Pi/2*x),x<0,
-(x+1)^3-1,x<8,-2*sin(x)-2):
g:=unapply(FF+1,x):
f:=x->g(x-5):

> p1:=plot(f(x),x= 0..11):

> PTS:=[.25,f(.25),`A`],[.6,f(.6),`B`],[2,f(2),`C`],
[2,f(2),`C`],[3,f(3),`D`],[4,f(4),`E`],[4.9,f(4.9),`F`],
[6.6,f(6.6),`G`],[8,f(8),`H`],[8.65,f(8.65),`I`],
[9.7,f(9.7),`J`]:

> txtPTS:=seq([z[1]+.2,z[2]+.3,z[3]],z=PTS):

> txt:=plots[textplot]({txtPTS},font=[TIMES,BOLD,12],
color=blue):

> dsks:= plot ({seq([z[1],z[2]],z=PTS)},color=red,style=POINT,
symbol=CIRCLE):

> p1:=plot(f(x),x= 0..11,color=blue,thickness=2):

> plots[display]({dsks,p1,txt},xtickmarks=[],
ytickmarks=[-2,-1,0,1,2],axesfont=[TIMES,BOLD,12]);