Describing Transformations of Radical Functions

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

Now, if we translate the graph horizontally $6$ units to the left, we obtain $y=\text{-}\sqrt{x+6}.$

Finally, let's translate the function vertically $6$ units down. This results in $f(x)=\text{-}\sqrt{x+6}-6.$

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