The graph of the function f(x) = x^2 will be shifted 2 units up, 1 unit left, and rotated 180 degrees. What is the resulting function g(x)?

g(x) = - (x+1)^2 +2

Step-by-step explanation:

1. Shifting up 2 units is y = x^2 + 2

2. Shifting to the left is y = (x + 1)^2

3. Rotating 180 degrees is just flipping the x-axis which means the whole equation becomes negative, y = -x^2

4. Therefore if you add it all up it becomes y = - (x+1)^2 +2

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