Question 1151528: Graph f(x)=square-root of x, then use transformations of that graph to graph h(x)=square root of x-1)-2. Label 3 points on your graph.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the graph of y = sqrt(x) and y = sqrt(x-1) - 2 is shown below.
the points that apply to y = sqrt(x) are (0,0), (4,2), (12,3.464).
the corresponding points that apply to y = sqrt(x-1) - 2 are (1,-2), (5,0), (13,1.464).
the graph of y = sqrt(x-1) is the same as the graph of y = sqrt(x) except that it is shifted to the right one unit.
the graph of y = sqrt(x-1) - 2 is the same as he graph of y = sqrt(x-1) - 2 except that it is shifted to the right one unit and down 2 units.
you can see that in the corresponding points.
(-0,0) from y = sqrt(x) becomes (1,-2) from y = sqrt(x-1) - 2
(4,2) becomes (5,0)
(12,3.464) becomes (13,1.464)
here's a reference on functons translations that contains information on concepts shown above plus more.
there are 5 pages involved so be sure to click on all to get complete coverage of the topic as they show it.
https://www.purplemath.com/modules/fcntrans.htm
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