SOLUTION: Please, I would appreciate your help. I have to graph y = sqrt (x+1) -3 and state the domain and range. thank you so much!

Algebra ->  Rational-functions -> SOLUTION: Please, I would appreciate your help. I have to graph y = sqrt (x+1) -3 and state the domain and range. thank you so much!      Log On


   

Question 527648: Please, I would appreciate your help.
I have to graph y = sqrt (x+1) -3 and state the domain and range.
thank you so much!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
y = sqrt%28x%2B1%29 - 3

First draw the graph of y = sqrt%28x%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Csqrt%28x%29%29

Next draw the graph of y = sqrt%28x%2B1%29
which is the red graph shifted left 1 unit to the left.  
That's the green graph below:

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Csqrt%28x%29%2Csqrt%28x%2B1%29%29

Finally draw the graph of y = sqrt%28x%2B1%29 - 3, which is the
green graph shifted 3 units down.  That's the blue graph below:

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Csqrt%28x%29%2Csqrt%28x%2B1%29%2Csqrt%28x%2B1%29-3%29

To find the domain, set the expression under the square root
radical ≧ 0.

   x + 1 ≧ 0
       x ≧ -1

This is the graph of the domain:



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 ≧ -3.


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


              

The interval notation for the range is 

[-3,infinity)

Edwin