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The graph of $ y = \sqrt{3x - x^2} $ is given. Use transformations to create a function whose graph is as shown.

2$\sqrt{3(x-2)-(x-2)^{2}}$

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Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

Okay, let's figure out what happened to change one graph to the other. What kinds of transformations? And then we can make changes to the equation. So noticed that the width of the original graph has not changed. It was three units wide, and it's still three units wide. However it hit it, hit it has shifted right? Two units also noticed that the height has changed. It was originally 1.5 units tall, and now it's three units tall. So that would be a vertical stretch. Times two by a factor of two. Okay, so to reflect that in the equation, the vertical stretch is going to be multiplying by two on the outside. And then the shift right to is going to be subtracting two from X and notice that we have X in two places. So we have to subtract two from each X, and that will be the equation of what we just have seen drawn