Question 158190
State the domain of the following and provide a brief explanation 
{{{f(x)=sqrt(x+4)}}}
<pre><font size = 4 color = "indigo"><b>
What is under a square root radical must never be negative,
To guarantee that, we set {{{x+4}}} greater than or equal 
to 0:

{{{x+4>=0}}}
  {{{x>=-4}}}

Now we draw a number line and graph the inequality {{{x>=-4}}}:

----------@===========================>
-7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5 

In interval notation that is {{{matrix(1,5,"[",-4,",",infinity,")")}}}

Now for an explanation, in case the above isn't sufficient,

let's draw the graph of 

{{{f(x)=sqrt(x+4)}}}

{{{drawing(450,200,-7,6,-1,4, graph(450,200,-7,6,-1,4,sqrt(x+4)),
line(-4,.1,7,.1),line(-4,-.1,7,-.1), line(-4,0,7,0),
locate(-4,.3,"@")

)}}}

Compare the domain on the number line above to the x-axis
on the graph of {{{f(x)=sqrt(x+4)}}}.  The domain is just the
"shadow" of the graph of {{{f(x)=sqrt(x+4)}}} upon the x-axis.

Edwin
AnlytcPhil@aol.com</pre></font></b>