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Describing Transformations of Radical Functions

Describing Transformations of Radical Functions 1.1 - Solution

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To write a function rule for the graph of the given function, let's first graph the parent function y=xy=\sqrt{x} in the same coordinate plane.

Now, if we translate the graph horizontally 4{\color{#009600}{4}} units to the right, we obtain y=x4.y= \sqrt{x-{\color{#009600}{4}}}.

Finally, let's translate the function vertically 6{\color{#0000FF}{6}} units down. This results in f(x)=x46.f(x)=\sqrt{x-4}-{\color{#0000FF}{6}}.

We can see that the last function matches the given graph. Thus, its equation is f(x)=x46.f(x)=\sqrt{x-4}-6.