Question 1143089
<pre>
{{{matrix(1,3,

"f(x)", ""="", 

system(matrix(3,3,1,if, -3<=x<3,abs(x),if,3<=x<9,sqrt(x), if, 9<=x<=11)))}}} 


Draw the graphs of

{{{red(y = 1)}}}, {{{green(y = abs(x))}}} and {{{blue(y = sqrt(x))}}}

{{{drawing(400,400,-3.9,11.9,-3.9,11.9,

graph(400,400,-3.9,11.9,-3.9,11.9,1,abs(x),sqrt(x)) )}}}


Draw vertical lines at the cut-off places -3, 3, 9, and 11

{{{red(y = 1)}}}, {{{green(y = abs(x))}}} and {{{blue(y = sqrt(x))}}}

{{{drawing(400,400,-3.9,11.9,-3.9,11.9,
line(-3,-4,-3,12), line(3,-4,3,12), line(9,-4,9,12), line(11,-4,11,12), 
graph(400,400,-3.9,11.9,-3.9,11.9,1,abs(x),sqrt(x)) )}}}  

Erase the graph of y=1 (the red one) everywhere except between x=-3 and 3, the first two vertical lines.

Erase the graph of y=|x| (the green one) everywhere except between x=3 and 9, the next two vertical lines.

Erase the graph of y=√<span style="text-decoration: overline">x</span> (the blue one) everywhere except between x=9 and 11, the last two vertical lines.

{{{drawing(400,400,-3.9,11.9,-3.9,11.9,
line(-3,-4,-3,12), line(3,-4,3,12), line(9,-4,9,12), line(11,-4,11,12), 
graph(400,400,-3.9,11.9,-3.9,11.9,

1*sqrt(x+3)*sqrt(3-x)/(sqrt(x+3)*sqrt(3-x)),
abs(x)*sqrt(x-3)*sqrt(9-x)/(sqrt(x-3)*sqrt(9-x)),
sqrt(x)*sqrt(x-9)*sqrt(11-x)/(sqrt(x-9)*sqrt(11-x))) 

)}}}

Erase the vertical cut-off lines, and put darkened or open circles at the
end points of each piece of the graph to indicate whether they are included or not:

{{{drawing(400,400,-3.9,11.9,-3.9,11.9,
 
red(circle(-3.02,1,.03),circle(-3.02,1,.07),circle(-3.02,1,.1),circle(-3.02,1,.15),circle(-3,1,.15),circle(-3.02,1,.15),circle(3,1,.16)),

green(circle(3,3,.03),circle(3,3,.07),circle(3,3,.1),circle(3,3,.15),circle(9,9,.16)),

blue(circle(11,sqrt(11),.03),circle(11,sqrt(11),.07),circle(11,sqrt(11),.1),circle(11,sqrt(11),.15),circle(11,sqrt(11),.15),circle(11,sqrt(11),.15),circle(11,sqrt(11),.16)),

blue(circle(9,sqrt(9),.03),circle(9,sqrt(9),.07),circle(9,sqrt(9),.1),circle(9,sqrt(9),.15),circle(9,sqrt(9),.15),circle(9,sqrt(9),.15),circle(9,sqrt(9),.16)),


graph(400,400,-3.9,11.9,-3.9,11.9,
1*sqrt(x+2.9)*sqrt(2.9-x)/(sqrt(x+2.9)*sqrt(2.9-x)),
abs(x)*sqrt(x-3.1)*sqrt(8.9-x)/(sqrt(x-3.1)*sqrt(8.9-x)),
sqrt(x)*sqrt(x-9)*sqrt(11-x)/(sqrt(x-9)*sqrt(11-x))) 

)}}}

Edwin</pre>