A circle has been transformed from the circle with equation \(x^2+y^2=1\). The equation for the transformed circle is \((x-3)^2+(y-5)^2=\frac19\).

1. What transformations were performed on the circle?
2. What are the center and radius of the new circle?

A circle has been transformed from a circle with equation \(x^2+y^2=1\). An equation for the transformed circle is \(x^2+2x+y^2-2y+\frac{14}9=0\).

1. What transformations were performed on the circle?
2. What are the center and radius of the transformed circle?

Describe the transformation from \(f(x)\) to \(g(x)\) if \(g(x)\) is equal to:

1. \(\text-\frac14f\left(\frac12x\right)+6\)
2. \(\text-f\left(\text-\frac23x\right)-12\)
3. \(6f(x-3)\)

Here is an equation of a parabola in standard form:

\(y=\frac13x^2+4x+19\)

1. Rewrite the equation in vertex form by completing the square.
2. Identify the transformations from the graph of \(y=x^2\) to this parabola.
3. Identify the vertex and \(y\)-intercept of this parabola.

What transformations will take the parabola \(y=x^2\) to the parabola \(y=\text-\frac32(x+18)^2-14\)?