SOLUTION: Please explain this to me. I have to graph each function and state it's domain and range. y = sqrt(x-3) + 3 and y = sqrt(x+1)-2 Thank you for taking the time to help me.

Question 525622: Please explain this to me.
I have to graph each function and state it's domain and range.
y = sqrt(x-3) + 3
and y = sqrt(x+1)-2
Thank you for taking the time to help me.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I have to graph each function and state it's domain and range.
y = sqrt(x-3) + 3
and y = sqrt(x+1)-2
**
y=√(x-3)+3
Domain:
Since there are no denominators, the only restriction is in the radical.
In all sqrts, the radican must be≥0
x-3≥0
x≥3
Domain:[3,∞)
Range:[3,∞) (basic √x curve bumped up 3 units)
..
Graphing:
Start with the basic √x with points at (0,0), (1,1) (9,3) and (16,4)
Move x coordinates 3 units to the right (3,0), (4,1) (12,3) and (19,4)
Finally, add 3 units to the y-coordinate: (3,3), (4,4) (12,6) and (19,7)
In effect, you are shifting the basic √x curve 3 units to the right and raising it 3 units vertically.
see graph below as a visual check on the answers:
..

..
y=√(x+1)-2
I will let you do this one.
The graph below can be a visual check on your answers:

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