Question 1199623
<pre>
{{{drawing(400,350,-11,11,-8.25,11,

graph(400,350,-11,11,-8.25,11,(x^2+14x+47)*sqrt(-x-5)/sqrt(-x-5)),

red(line(-5,2,0,2), line(3.3,-8,6,-8), circle(-5,2,.3),circle(-5,2,.1),circle(-5,2,.2),
circle(0,2,.3),circle(0,2,.1),circle(0,2,.2),
circle(6,-8,.3),circle(6,-8,.1),circle(6,-8,.2),
circle(3,-8,.3)

)

 )}}}

DOMAIN:
Project the graph from both above the x-axis and from below the x-axis ONTO the
x-axis to find the domain. That's the union of the two blue intervals on the 
x-axis below. We include 0 and 6, so we put "]" after them. We don't include 3
or negative infinity, so we put "(" before them. 

{{{drawing(400,350,-11,11,-8.25,11,

graph(400,350,-11,11,-8.25,11,(x^2+14x+47)*sqrt(-x-5)/sqrt(-x-5)),

red(line(-5,2,0,2), line(3.3,-8,6,-8), circle(-5,2,.3),circle(-5,2,.1),circle(-5,2,.2),
circle(0,2,.3),circle(0,2,.1),circle(0,2,.2),
circle(6,-8,.3),circle(6,-8,.1),circle(6,-8,.2),
circle(3,-8,.3)),blue( 

line(-12,0,0,0), line(3.3,0,6,0),

line(-10.5,.5,-11,0), line(-10.5,-.5,-11,0),
circle(0,0,.3),circle(0,0,.1),circle(0,0,.2),
circle(6,0,.3),circle(6,0,.1),circle(6,0,.2),
circle(3,0,.3)   )





 )}}}

So the domain is 
{{{matrix(1,11,  "(" , -infinity, "," , 0 , "]" ,U, "(" ,3, "," ,6,"]")}}}

RANGE:
Project the graph from both the left of the y-axis and from the right of the 
y-axis ONTO the y-axis to find the range. Notice that the horizontal line
segment at the bottom right of the graph projects only onto the single point at
-8 on the y-axis. So we just put braces around it like this {-8}. Then we take
the union of the set containing that single number and the blue interval on the
y-axis from -2 to infinity. We include -2, so we put "[" before it. But we don't
include infinity, so we put ")" after it.

{{{drawing(400,350,-11,11,-8.25,11,

graph(400,350,-11,11,-8.25,11,(x^2+14x+47)*sqrt(-x-5)/sqrt(-x-5)),

red(line(-5,2,0,2), line(3.3,-8,6,-8), circle(-5,2,.3),circle(-5,2,.1),circle(-5,2,.2),
circle(0,2,.3),circle(0,2,.1),circle(0,2,.2),
circle(6,-8,.3),circle(6,-8,.1),circle(6,-8,.2),
circle(3,-8,.3)),blue( 

line(0,-2,0,12),

line(-.5,10.5,0,11), line(.5,10.5,0,11),
circle(0,-8,.3),circle(0,-8,.1),circle(0,-8,.2),

circle(0,-2,.3),circle(0,-2,.1),circle(0,-2,.2)

   )





 )}}}

So the range is 
{{{matrix(1,9,  "{" , -8, "}", U , "[" , -2 , "," , infinity,")")}}}

Edwin</pre>