Final answer:
The graph of the function y = 2(x-3)² - 3 is transformed by dilation and reflection. Dilation stretches the graph vertically, while reflection flips the graph across the x-axis.
Step-by-step explanation:
The graph of the function y = 2(x-3)² - 3 can be transformed using dilation and reflection.
Dilation occurs when the function is multiplied by a constant to stretch or compress the graph. In this case, the function is multiplied by 2, which stretches the graph vertically. The vertex of the parabola remains the same, but the amplitude is doubled.
Reflection occurs when the function is multiplied by -1 to flip the graph across the x-axis. In this case, the entire function is multiplied by -1. This causes the graph to be reflected over the x-axis.