Given:

The graph of \(f(x) = sqrt(16−x^2)\)

To determine :

The equation of transformed graph shown in the given figure.

The parent graph of \(f(x) = sqrt(16−x^2)\).

Since the graph is shifted vertically down by 1 unit.

Therefore, the equation becomes,

\(f(x) =sqrt(16-x^2)-1\)

Also, the graph is a reflected graph in the x - axis . Hence we have

\(f(x) =sqrt(16−x^2)− 1\)

Now, the graph is has a vertical compression by 4 units.

Therefore, the transformed graph is \(f(x) =− 1/4sqrt(16-x^2)-1\)