SOLUTION: Graph {{{y=sqrt(x+3)-3}}} by using {{{y=sqrt(x)}}}

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Question 147596: Graph y=sqrt%28x%2B3%29-3 by using y=sqrt%28x%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the graph of y=sqrt%28x%29


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x%29%29+ Graph of y=sqrt%28x%29


Now it turns out that if you generate a table for the equation of y=sqrt%28x%2B3%29, then you'll see that the graph is shifted 3 units to the left like this


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x%29%2Csqrt%28x%2B3%29%29+ Graph of y=sqrt%28x%29 (red) and the new graph y=sqrt%28x%2B3%29 (green) that has been shifted 3 units to the left.


Now subtracting 3 from the entire equation gives you y=sqrt%28x%2B3%29-3 which will shift the entire graph of y=sqrt%28x%2B3%29 down 3 units.



So we end up with

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x%29%2Csqrt%28x%2B3%29-3%29+ Graph of y=sqrt%28x%29 (red) and the new graph y=sqrt%28x%2B3%29-3 (green) that has been shifted 3 units to the left and 3 units down.