Question 525623: I would really appreciate your help.
I'm not sure how to go about this.
I have to graph each function and state it's domain and range.
y = sqrt (x+2) -2
Thanks so much.
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+2) -2
**
y=√(x+2)-2
Domain:
Since there are no denominators, the only restriction is in the radical.
In all sqrts, the radican must be≥0
x+2≥0
x≥-2
Domain:[-2,∞)
Range:[-2,∞) (basic √x curve moved down 2 units)
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Graphing: Selecting four convenient points on the curve:
Start with the basic √x with points at (0,0), (1,1) (9,3) and (16,4)
Move x coordinates 2 units to the left (-2,0), (-1,1) (7,3) and (14,4)
Finally, minus 2 units from the y-coordinate: (-2,-2), (-1,-1) (7,1) and (14,2)
In effect, you are shifting the basic √x curve two units to the left and dropping it 2 units vertically.
see graph below as a visual check on the answers:
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