SOLUTION: State the domain of the following and provide a brief explanation f(x)=square root x+4

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Question 158190: State the domain of the following and provide a brief explanation
f(x)=square root x+4
Answer by Edwin McCravy(3581) About Me  (Show Source):
You can put this solution on YOUR website!
State the domain of the following and provide a brief explanation
f%28x%29=sqrt%28x%2B4%29

What is under a square root radical must never be negative,
To guarantee that, we set x%2B4 greater than or equal 
to 0:

x%2B4%3E=0
  x%3E=-4

Now we draw a number line and graph the inequality x%3E=-4:

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

In interval notation that is matrix%281%2C5%2C%27%5B%27%2C-4%2C%27%2C%27%2Cinfinity%2C%27%29%27%29

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

let's draw the graph of 

f%28x%29=sqrt%28x%2B4%29

drawing%28450%2C200%2C-7%2C6%2C-1%2C4%2C+graph%28450%2C200%2C-7%2C6%2C-1%2C4%2Csqrt%28x%2B4%29%29%2C%0D%0Aline%28-4%2C.1%2C7%2C.1%29%2Cline%28-4%2C-.1%2C7%2C-.1%29%2C+line%28-4%2C0%2C7%2C0%29%2C%0D%0Alocate%28-4%2C.3%2C%27@%27%29%0D%0A%0D%0A%29

Compare the domain on the number line above to the x-axis
on the graph of f%28x%29=sqrt%28x%2B4%29.  The domain is just the
"shadow" of the graph of f%28x%29=sqrt%28x%2B4%29 upon the x-axis.

Edwin
AnlytcPhil@aol.com