Question 527648
<pre>
y = {{{sqrt(x+1)}}} - 3

First draw the graph of y = {{{sqrt(x)}}}

{{{graph(400,400,-5,5,-5,5,sqrt(x))}}}

Next draw the graph of y = {{{sqrt(x+1)}}}
which is the red graph shifted left 1 unit to the left.  
That's the green graph below:

{{{graph(400,400,-5,5,-5,5,sqrt(x),sqrt(x+1))}}}

Finally draw the graph of y = {{{sqrt(x+1)}}} - 3, which is the
green graph shifted 3 units down.  That's the blue graph below:

{{{graph(400,400,-5,5,-5,5,sqrt(x),sqrt(x+1),sqrt(x+1)-3)}}}

To find the domain, set the expression under the square root
radical &#8807; 0.

   x + 1 &#8807; 0
       x &#8807; -1

This is the graph of the domain:

{{{drawing(400,100,-20,20,-2,1,number_line( 400, -5, 5),
locate(-4.3,.5,"[=============================>")


)}}}

This is the interval notation for the domain:

 [-1,{{{infinity}}})

The range is from the lowest value of y, which is -3 to infinity,
represented by the inequality y &#8807; -3.


the green part of the vertical number line below is the graph of
the range


              {{{drawing(50,400,-2,2,-5,5,graph(50,400,-2,2,-5,5), 
circle(0,-3,.2),circle(0,-3,.175),circle(0,-3,.15),circle(0,-5,.1),
circle(0,-3,.25),circle(0,-3,.3),green(line(0,-3,0,4.9))



)

}}}

The interval notation for the range is 

[-3,{{{infinity}}})

Edwin</pre>