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# Describing Transformations of Radical Functions

## Describing Transformations of Radical Functions 1.1 - Solution

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

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

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

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