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The parent function f(x) has

a square root function with a domain of x greater than or equal to 0

and a range of y greater than or equal to 0

First, what do we know about f(x)?

Now look at the changes that g(x) introduces into the graph.

(x-7) inside the square root causes a horiztonal shift of 7 units to the right

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Having a coefficient of -7 gives a vertical compression by a factor of 7

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Summary:

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g(x) is obtained by applying a horizontal shift of 7 units to the right and a vertical compression by a factor of 7 to f(x)

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